Category: Exam Questions

M.I.T. General Exams in Macroeconomics, 1959-71

Post author By Irwin Collier
Post date 2016-12-24

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The original plan of Economics in the Rear-View Mirror was to provide a single artifact for each post. Larger (composite) data sets are given dedicated pages (e.g. Harvard Ph.D.’s in economics 1875-1926; Chicago Ph.D.’s in economics 1894-1926; Economics Rare Book Reading Room). Sometimes I come along a group of artifacts that are best kept together so I end up with a post like today’s that prints out as more than 25 pages of text.

Today’s treasure is a fairly complete run of MIT general examination questions in macroeconomics for the period 1959-1971 found in a folder in the Evsey Domar papers at the Economists’ Papers Archive at Duke University. For a few of the exams we even have handwritten records indicating the questions chosen by the examinees and the grades awarded (I have omitted the names).

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May 22, 1959
General Examination in Macroeconomics

Answer four questions, including at least one from each group.

I.

(a) Explain the basic economic philosophy which forms the foundation of modern national income (and gross product) estimates in Western countries.
(b) Show how this philosophy is transformed into specific criteria used by the U.S. Department of Commerce in their estimates of Gross National Product, National Income, and Consumer Disposable Income. Be as specific as you can.
Present a careful analysis of the problem of “Price Flexibility and Employment” and trace its discussion (that is, of its principal points) through economic literature beginning with Keynes’ General Theory.
What practical conclusions follow from this discussion?
It was repeatedly said in 1946 that “Increased production is the best cure against inflation.” Comment on this statement as completely as you can. (Hint: Consider the dual aspect of the production process.) In the light of your finding, do you think a labor strike to be deflationary or inflationary?

II.

Construct a “flexible” multiplier-accelerator model in which the government plays an active role. That is, it levies a proportional income tax and engages in stabilizing expenditures.
1. Imagine first that the tax on last year’s income is collected this year, while consumers recon their disposable income on a cash basis (i.e. income earned minus taxes actually paid). Government expenditures are constant. How do changes in the tax rate affect the behavior of the model?
2. If the tax system should go on a withholding basis, so that the tax on this year’s income is collected this year, how does that affect the stability and other characteristics?
3. Taking taxes as in (b), suppose government expenditures are proportioned to the gap between full employment income and last year’s income. Is this stabilizing?
4. Suppose government outlays are a decreasing linear function of the observed rate of change of income. Is this stabilizing?
It is often said that the cause of any depression is the previous boom and its “excesses.” Does this make sense in terms of modern business cycle theory?

III.

“The purpose of taxation is never to raise money but to leave less in the hands of the taxpayer.” Comment fully and critically. Can you identify the author? (No great penalty if you cannot.)
To the best of your ability, try to analyze the incidence of a corporate income tax. What empirical information would you need for this purpose? (Please be reasonable).
“People are always willing to become wealthier. The problem of economic growth in advanced countries is: will the public be willing to add to its holdings of physical assets an amount equal to the unconsumed portion of full employment output?” Discuss fully including a description of the alternatives to holding physical assets, the efficacy of the price system, policy measures.

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February 8, 1960
GENERAL EXAMINATION IN ECONOMIC THEORY

For the old-style exam (microeconomics alone), answer the first question (one hour) and any three of the others in Part I (two hours). For the new-style exam, answer any three questions in Part I (two hours) and any three questions in Part II (two hours), but without including both 3 and 4. Use separate books for Parts I and II.

PART I

In a purely competitive economy, the only goods are food (F) and clothing(C), and the only factors are labor (L) and land (T), both fixed in supply. Each household supplies either L or T, but not both. Both goods are produced at constant returns to scale with both L and T. Isoquants are normally curved for both products; and, at any given marginal rate of substitution, a higher ratio of T to L is implied for F than for C.
1. Show how the economy’s transformation curve for F and C is derived. Could it be either concave or convex or linear, and why?
2. If everyone in the economy always divides his income equally between F and C, show how this determines uniquely what goods are produced, how they are produced, and for whom.
3. How is that general equilibrium modified if the government imposes a tax on F and distributes the entire proceeds equally among all of the labor-supplying households. (Assume for simplicity that the tax and subsidy involve no administrative costs.)
4. Would there be better ways of achieving the same redistribution of income? Explain fully why or why not.
The demand for a monopolist’s produce is given by p = 50 – .001q. Within the relevant range, his total cost as a function of his output is C = 40q – .0005q².
1. In the monopolist’s long-run equilibrium, what are his price, output, and profit?
2. How are those magnitudes affected if demand now increases to p= 56 – .001q?
3. In general, what factors determine whether a monopolist’s equilibrium price will rise or fall in response to an increase in demand? Explain how the actual result in the present example fits in with those general principles.
Plant capacity for a certain product costs $6 per year per unit of output. Given a plant of any particular size, any output up to the capacity level can be produced at a variable cost of $12 per unit; and outputs in excess of capacity are impossible. Demand is given by p = 24 – .001q (where p is the price of the product in dollars per unit and q is the quantity of product demanded per year).
1. What are the long-run-equilibrium prices, outputs, and profits under conditions of (i) monopoly and (ii) pure competition?
2. How are those equilibrium magnitudes affected in both the short and long run if new technological knowledge suddenly makes it possible to produce the product with a new type of equipment at a capacity cost of $5 per year per unit of output and a variable cost of $9 per unit of output. (Assume that, in the short run, new capacity can be added but none of the pre-existing capacity wears out. In the long run, all of the old capacity does wear out.)
Show how an individual’s labor-supply curve can be derived from his basic preferences for leisure and income, assuming that he also has a fixed income from other sources. Then show the comparative effects of three alternative taxes that might be imposed to extract the same revenue from this man: (a) a lump-sum or poll tax, (b) a proportional income tax, and (c) a progressive income tax.
Summarize Ricardo’s theory of rent, and evaluate its correctness and realistic relevance. In what sense, if any, does rent not enter into cost? Explain carefully.

PART II

Discuss the role played by population growth in modern theories of economic development and business cycles. Be specific.
Write an essay on the subject of “The General Theory After Twenty-Five (almost) Years.” Include in it, among other things, your evaluation of the usefulness of the book from the point of view of: (a) an advanced capitalist economy like the U.S.; (b) an underdeveloped mixed economy like India; (c) a centrally directed socialist economy like the USSR.
Present your favorite theory (traditional, eclectic or entirely original) of the business cycle. Explain the empirical tests which you would subject it to. Be specific.
Present an explanation of the causes of the current inflation in this country. Indicate the empirical tests which your explanation would have to pass. Be specific.
(a) Explain the reasons why the economic activities of the government create special problems in national income (or gross product) accounting. Analyze critically the treatment of these problems by the U.S. Department of Commerce.
(b) “Existing methods of international comparisons of per capita national income have an upward bias in favor of advanced countries.” Comment. “Don’t forget to indicate what these methods are.)

Comprehensive Exam Grades in Macro Theory
MIT Feb. 1960

[Student]	Q1	Q2	Q3	Q4	Q5	Average	Remarks
[1]	50 (F)		30 (F)		60(D)	F+	Fail
[2]		60(C-)	20(F-)	60(C-)		D ?	[guess: “Directed information to who? , ≥4 fail”]
[3]		70 (C)	65 (C)		70 (C)	C	Fair –
[4]	70 (C)		70 (C)			C	Fair –

A: 90-100
B: 75-89
C: 60-74
D: 50-59
F: less than 50

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September 19, 1960
General Examination in MACROECONOMICS

Answer three questions; at least one from each part.

I.

Discuss Savings as an economic problem.
a. Write an essay on the subject of “The Problem of Intermediate Products in National Income and Product Accounting.” Be as comprehensive as you can.
b. Compare briefly the treatment of intermediate products in the Input-Output and Flow-of-Funds systems.
Write a comprehensive essay on the subject of “The Economic Significance of the Rate of Interest.”

II.

Write on the capital-output ratio as a tool for economic analysis, including some comment on:
1. The problem of defining, measuring and interpreting the concept.
2. Known facts about the historical course of the ratio..
3. The role the concept plays in theories of growth and fluctuations.
What are the facts about the relative magnitude of cyclical fluctuations in the output of capital goods and consumer goods? What are the theoretical implications of the facts as you know them? Discuss in this light the mildness of post-war economic fluctuation in the U.S.
Write an essay on the contribution to the theory of economic growth of one of the following: Wicksell, Schumpeter, Kaldor, Tobin.

Macroeconomics Grades
Sep. 1960

	Part I			Part II			Aver.
	Q1	Q2	Q3	Q1	Q2	Q3
[1]			G-	G-		F+/G-	G-
[2]	G		F+	F-/Fail
[3]	G+		F+	G-			G-
[4]	G+		G/G+	G-			G/G+
[5]			G	G+	G-		G
[6]		G	G			G	G

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February 6, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Part II—Macroeconomics—Two Hours

Answer THREE questions, at least ONE from each Part. Use a separate examination book for each question.

Part I.

Write a comprehensive essay on the subject of “International Comparisons of National Income and Product”.
Discuss saving as an economic problem. Trace the treatment of saving in the relevant economic literature.
Write a comprehensive essay on the subject of “The Economic Significance of the Rate of Interest”.

Part II.

Assume that inventory behavior is governed in the following Metzlerian way:
1. Desired inventory is proportional to expected sales.
2. Planned inventory investment behaves according to the capital stock adjustment principle (“flexible acceleration”).
3. Expected sales equal last period’s sales.
4. Current sales are proportional to current income, with unexpected sales made from stock.
5. Income is the sum of Sales, exogenous government and fixed investment expenditures, and inventory investment (including unplanned!).

Now suppose operations research succeeds in (i) reducing the desired inventory-sales ratio and (ii) increasing the speed of adjustment. What effects will this have on the cyclical behavior of the system?

Discuss the role of (i) floors and ceilings and (ii) autonomous investment in theories of growth and fluctuation, and say something about the realism of each concept.
Formulate a one-sector model of economic growth using the following assumptions:
1. One commodity, usable either as consumer good or as capital good.
2. Its output is given by a production function with the stock of the capital good and labor as inputs, under constant returns to scale. (Consider various degrees of substitutability.)
3. Depreciation proportional to stock of capital.
4. Supply of labor grows geometrically, and exogenously, and is inelastically supplied.
5. Competitive profit-maximizing rules.
6. All profits are saved, all wages consumed.

Within this model, discuss the properties of the full-employment growth path (i.e. the development of output capital, wages, etc., which will equate desired saving and investment at full employment).

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May 22, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two Hours

Answer THREE questions, at least ONE from each part. (Course XV students answer ONE question from each part only.) USE A SEPARATE EXAMINATION BOOK FOR EACH QUESTION.

Part I.

Write a comprehensive essay on the subject of “The Measurement of Economic Growth”. Include in it the description of existing methods, their rationale (the most important part) and your suggestions for improvement.
Write an essay on “The General Theory after Twenty-Five Years”.
a. Explain the nature and the rationale of the definition of the concept of money in “Price Flexibility and Employment” problems.
b. “If the ‘Balanced-Budget Multiplier’ is correct, isn’t Say’s Law also correct?” Comment fully.

Part II.

“By making existing capital assets obsolete, technological progress is alleged to create new investment opportunities and thus raise the level of income and employment. But to the extent that such obsolescence was foreseen, the assets were depreciated over a shorter period and thus gave rise to larger gross savings. Therefore, expected technological progress fails to stimulate the economy.” Comment fully.
Present your favorite (traditional, eclectic, or original) business cycle theory. Indicate the empirical tests to which it will be subjected.
“In order to prevent a cost-push inflation, wage rates in each firm or industry should not increase faster than its labor productivity; price increases will thus be avoided.”
Comment fully and critically; indicate and justify your wage and price policy.

General Exam Grades “MacroTheory” May 22, 1961

	[Part] I			[Part] II
[Student]	Q1	Q2	Q3	Q4	Q5	Q6	Average
[1]		G	G-/F+	F+			G-
[2]	G-				G-/F+	F-	F+
[3]		F+	G-		G		G-
[4]	E-				G-	E-	G+
[5]			G+		G-	F	G-
[6]	E-/G+	G		F			G
[7]			G+	G-		F-	G-
[8]	E-	E-			G+		E-
[9]			Failed		F	F-/Failed	Fail+
[10]	F+	G			G-		G-
[11]		G			G	F-	G-
[12]		G-			G-/F+	F-	F+
[13]	F+		G-		G		G-
[14]		G+	G-		G		G
[15]	Failed	G			G-/F+		F+

[16]			F-/Failed		Failed		Failed
[17]		G-/F+			F		F+

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September 18, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two Hours

Answer FOUR questions, TWO from each part. USE A SEPARATE EXAMINATION BOOK FOR EACH QUESTION.

Part I.

State, explain and justify the treatment of government expenditures (Federal, state and local) in the computation of national product and its components. Why is government treated differently from other sectors? What is the logical foundation for such treatment?
Compare and contrast the Keynesian and the so-called Classical systems.
Contrast the investment criteria applicable to (a) an individual firm, (b) the U.S. government, (c) the government of an undeveloped country. Explain clearly your reasons for such differences, if any.
Write an essay on “The History of the Consumption Function.” Indicate and evaluate the major contributions. How significant are they? Which one do you prefer and why?

Part II.

Describe fully the “economic indicator” approach to economic forecasting. Evaluate its performance. Compare it with the use of projected models of GNP.
Describe the long-term trends in (a) population, (b) output, (c) capital, (d) real wage rates, (e) interest, (f) relative shares, (g) capital-output and other important ratios. What constancies have people claimed to observe? What behavior is explicable by a simple neoclassical model? What points to technological change or to various non-neoclassical growth theories? Mention authors as well as theories.
Summarize briefly the historical facts on business cycles or fluctuations here and abroad. What theories have been suggested? Besides naming names, give your own best way of cataloguing the different theories (e.g. non-linear, etc.).
Give the basic facts on “growth” here and abroad, recently and in history. How could America increase its sustained growth rate? Be analytical and specific.

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February 5, 1962
GENERAL EXAMINATION IN ECONOMIC THEORY
Part II—Macroeconomics
TWO HOURS

Please answer THREE questions, at least ONE from each Part. Use a separate examination book for each question.

Part I.

“Existing methods of national product computation exaggerate the rate of growth of real product over time in a given country, and overstate the ratio between the real product of highly developed and of undeveloped countries.”
Comment fully.
Compare and contrast the economic effects (on growth and level of income, employment, income distribution, and on any other phenomena you consider important) of population growth and of the growth of the capital stock.
a.Explain the basic assumptions and reasoning used in the “Price Flexibility and Employment” discussions. (If you can, identify the authors involved.)
b. Explain the nature and definition of the concept of money used in the same discussions.
c. “If the ‘Balanced-Budget Multiplier’ is correct, isn’t Say’s Law also correct?” Comment fully..

Part II.

Analyze a one-sector growth model in which net output is produced by labor and capital by a smooth neoclassical constant-returns-to-scale aggregate production function experiencing no technical change. Net output is divided up into consumption and net capital formation (or investment). Consumption, according to Modigliani, is 100 per cent of income when the capital wealth-to-output ratio is, say, 3, being a fraction at lower ratios and exceeding unity at higher ratios.
1. First, let labor supply be stationary. Starting with very low capital, describe the evolution of the system’s output, wage rate, interest rate, capital, and various ratios (Q, w, r, k, k/L, Q/L, Q/k, wL/rk, etc.)
2. Do the same if labor will always grow at 2 per cent per year.
Describe and contrast business cycle approaches of (a) The National Bureau of Economic Research, (b) Econometricians like Tinbergen and Klein, (c) other typical modern Evaluate with respect to policy, prediction, explanation and present-day relevance.
How can President Kennedy increase “growth” in a world with problems of international payments, possible wage-price “creeps,” fiscal burdens for defense, and stubborn productivity and personal thrift patterns. Prescribe, diagnose, and compromise dilemmas if there are any.

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May, 1962
GENERAL EXAMINATION—MACROECONOMICS

Answer three questions, including at least one from each part.

PART I

a. Write an essay on the subject of “The Problem of Intermediate Goods in National Income and Product Accounting”.
b. Suppose you were asked to compute national income and product for an economy consisting of a Prince and a number of slaves, from the point of view of the Prince. Explain the modifications of the usual methods that this assignment will require. Do you think it will result in a larger or a smaller income?
A critic of Keynes’ General Theory once said that “What is new in it is wrong, and what is right is old”.
Comment fully.
“The problem of price flexibility and employment is a silly game based on the inclusion of some debtor-creditor relationships and the exclusion of others”.
Comment fully.

PART II

Is an economy which has been growing at full employment (and full utilization of capacity) helped or hindered in the maintenance of full employment (and utilization) by a more rapid rate of growth of the labor force?
It is sometimes said that the widespread adoption of scientific inventory control, permitting lower inventory-sales ratios on the average, will have the effect of damping inventory fluctuations. Discuss this theoretically. Do the same for the advent of improved forecasting methods.
Discuss the relation between the propensity to save and the rate at which potential output increases.

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September 17, 1962
GENERAL EXAMINATION IN ECONOMIC THEORY
Part B—Macroeconomics

TWO HOURS

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

Part I

Write an essay on the role of microeconomics in the construction and the testing of macroeconomic theory.

Part II

Discuss and evaluate the treatment of government in the U.S. National income Accounts. Give special emphasis to the problems involved in using the figures for intertemporal and international comparison of the role of government both as a user of resources and as a producer.
Write an essay on the “history, nature and significance” of the consumption function.

Part III

Discuss the issues of concept, theory, inference, and measurement that are involved in estimating the relation between investment and the growth of potential output.
What is your theory of inflation? How does it tie in with modern business cycle theory?

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GENERAL EXAMINATION IN MACROECONOMICS
February 4, 1963

ANSWER ONE QUESTION FROM EACH PART (THREE QUESTIONS IN ALL).

Part I.

Suppose that in an economy in equilibrium a large number of enterprises operating as proprietorships and partnerships decide to incorporate.
1. List the principal ways in which the national income accounts might be affected in the short run. (Make explicit any reasonable assumptions you may want to make about real changes in the flows of spending and income.)
2. What fallacious conclusions might you draw as to structural changes in the economy from these changes in the accounts if you did not know their source?
Explain the basic economic philosophy which forms the foundation of national income and product estimates in the United States. Indicate how this philosophy is applied by the Department of Commerce in its estimates of Gross National Product, National income, and Disposable Income. (Be specific.)

Part II.

Discuss, making use of an explicit model of income-determination, the various ways in which prices and wage rates enter into the determination of national income. In particular, what are the issues of theory and fact which are relevant to the debate about “underemployment equilibrium”?
Identify and discuss, briefly and concisely, the nub of the issues raised by each of the following (where appropriate use an explicit model)
1. “The rate of interest bears no necessary relation to the quantity or value of the money in circulation. The permanent amount of the circulating medium, whether great or small, affects only prices; not the rate of interest.” (J. S. Mill)
2. “If it is true that the marginal propensity to consume of wage earners is higher than of profit recipients, one way to cure a deflationary gap and unemployment is to raise the money wage rate.”
3. “Increased production is the best cure against inflation.”
4. “The cause of any depression is the previous boom and its “excesses”.”

Part III.

Discuss the critical issues of fact, theory, and value that are involved in designing a fiscal-monetary policy for the United States for the mid-1960’s. Elaborate, in particular, the criteria in terms of which you (“as economist”) would evaluate any particular mix of instruments.

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General Examination in Macroeconomics
May 13, 1963

Answer three questions in all, including at least one from each part.

I.

In the earlier postwar period it was often said that “Increased production is the best cure against inflation.” Comment on this statement. In the light of your comment, do you think a prolonged strike is inflationary or deflationary?
a. Set up a reasonable aggregative model appropriate to a closed economy where the money wage rate is rigid ownwards (only downwards).
b. Assuming that the initial equilibrium configuration yields “full employment” and that the money wage rate cannot fall below the initial equilibrium wage rate, trace the effects on the critical variables of

(i) an increase in the nominal stock of money

(ii) a decrease in the nominal stock of money

(iii) an autonomous fall in the volume of investment

c. In each case, how would your answers differ, especially as regards the possibility of “under-employment equilibrium”, if the money wage rate, as well as all other prices, were fully flexible?
d. How would your answers differ if money wage rates were governed by two-way escalator clauses?
Write an essay on the theoretical and empirical foundations of an eclectic macroeconomic theory of demand for investment.

II.

In Kaldoria, the marginal (=average) propensities to save out of wages and out of non-wages are different. The latter exceeds the former by a considerable margin. Together wages and non-wages exhaust national income. Markets are such that when national income exceeds a certain value Y*, the share of profits in national income tends to rise, and when national income falls short of Y*, the share of profits tends to fall. Finally, all investment is exogenous.
1. Show that Y* is a stable level of national income.
2. Calculate the share of profits when national income is Y*.
3. Can you think of any reasons why Y* should correspond to “full employment”?
4. Discuss the factual validity of the theory. That is, does Kaldoria resemble any country you know well?
5. Can you modify the theory to include a marginal propensity to invest out of profits?
Suppose investment behavior is such that all investment opportunities which offer a rate of return greater than or equal to some fixed target rate R are instantly adopted. Labor and capital are the only factors of production and constant returns to scale prevail. (Use a Cobb-Douglas production function, if you like.) The labor force grows exogenously at a fixed annual rate g.
1. What saving rate, relative to national product, will just maintain full employment equilibrium?
2. How does that saving rate vary with g?
3. What do you make of the common notion that a rapidly-increasing labor force makes it harder to maintain full employment?
Describe the approximate timing of inventory investment during postwar American business cycles, and compare this with the results of some formal model of inventory fluctuations.

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September 16, 1963
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

Please answer THREE QUESTIONS, at least ONE from each part. Use a separate examination book for each question.

Part I.

a. Write an essay on the subject of “The Problem of Intermediate Goods in National Income and Product Accounting”.
b. Suppose you were asked to compute national income and product for an economy consisting of a Prince and a number of slaves, from the point of view of the Prince. Explain the modifications of the usual methods that this assignment will require. Do you think it will result in a larger or a smaller income?
A critic of Keynes’ General Theory once said that “What is new in it is wrong, and what is right is old”.
Comment fully.
a. Explain the nature and the rationale of the definition of money in “Price Flexibility and Employment” problems.
b. “If the ‘Balanced-Budge Multiplier’ is correct, isn’t Say’s Law also correct?”
Comment fully. Explain the nature of both propositions.

Part II.

Discuss the role of (a) floors and ceilings and (b) autonomous investment in theories of growth and fluctuations.
Indicate the empirical tests to which the propositions expounded by you can be subjected.
“In order to prevent a cost-push inflation, wage rates in each firm or industry should not increase faster than labor productivity.”
Comment fully and critically. Indicate and justify your wage and price policy to achieve economic growth and stability.
Explain and compare the roles which the growth of population and the growth of capital (separately and together) play in modern growth and business cycle theory.

General Examination Grades in Macroeconomics September 1963

	Questions
Student	1	2	3	4	5	6	Total	Grade
[1]	18	25				22	65	Fair
[2]	29				24	26	79	G
[3]	30	29				29	88	E-
[4]	22		20			23	65	Fair
[5]			29	24		25	78	G

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February, 1964
GENERAL EXAMINATION IN ECONOMIC THEORY
MACROECONOMICS—TWO HOURS
[Note: this exam recycled in February, 1968]

Answer THREE QUESTIONS, at least ONE from each part. Use a separate examination book for each question.

Part I

Write a comprehensive essay on the subject of “Comparisons of National Income and Product in Time and Space.” Indicate the biases which arise in such comparisons.
“The problem of price flexibility and employment is a silly game based on the inclusion of some debtor-creditor relationships and the exclusion of others.” Comment fully. Indicate what definition of money used in your discussion.
Write a comprehensive essay on the subject of “The Interrelationships between Money, Prices and the Rate of Interest.” Include brief reviews of the relevant theories.

Part II

“In order to prevent a cost-push inflation, wage rates in each firm or industry should not increase faster than its labor productivity.” Comment fully.
“If Hansen is correct, the faster is the rate of growth of population, the lower will be the unemployment level in the U.S.” Discuss fully. Include natural growth of population and immigration. In what respect does the growth of population differ from that of the stock of capital?
Write an essay on “Floors and Ceilings in Business Cycle Theory.” Indicate the specific theories and your methods of testing each.

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February 8, 1965
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

Part I.

Write an essay on the subject of “Keynes and Patinkin on the Relation between the Quantity of Money on the One Hand, and Interest Rate, Price Level and National Income on the other.”
It is frequently said that existing methods of national income computations exaggerate the present-day American per capita income in comparison with that of less developed countries and in comparison with American income in the past. Comment fully and critically. Are there statistical methods which may impart an opposite bias?
Compare and contrast the economic effects (on growth and level of income, employment, income distribution, and on any other economic phenomena you consider important) of population growth and of the growth of the capital stock.

Part II.

1. According to the 1965 Economic Report of the President:
  1. “The general guide for wages is that the percentage increase in total employee compensation per man-hour be equal to the national trend rate of increase in output per man-hour.”
  2. “The general guide for prices calls for stable prices in industries enjoying the same productivity growth as the average for the economy; rising prices in industries with smaller than average productivity gains; and declining prices in industries with greater than average productivity gains.” (p. 108)
    1. What would this policy imply for:
      1. average unit labor costs
      2. average product prices
      3. income distribution
      4. labor allocation among industries and skills
    2. According to theories of inflation you find most persuasive, what aspects of the price-wage mechanism would be most likely to frustrate the Council guideposts that are outlined above?
  1. The U. S. economic recovery from 1961 to the present has been accompanied by less inventory investment, especially in manufacturing, than occurred in previous recoveries. Some pertinent data are presented below.

	Manufacturing
	(Monthly averages for year) $ billions
	Sales	Inventories	Ratio
1950	18.6	31.0	1.48
1951	21.7	39.3	1.66
1952	22.5	41.1	1.79
1953	24.8	43.9	1.76
1954	23.3	41.6	1.81
1955	26.4	45.0	1.62
1956	27.7	50.6	1.73
1957	28.7	51.8	1.80
1958	27.2	50.0	1.84
1959	30.2	52.7	1.70
1960	30.8	53.8	1.76
1961	30.9	55.1	1.74
1962	33.3	57.7	1.70
1963	34.7	60.1	1.69
1964	37.1	62.2	1.64

Source: 1965 Economic Report, p. 237.

It has been said that this development has

1. substantially improved the ability of the economy to avoid a recession;
2. made it more likely that if a recession does occur, that it will be milder than it would otherwise have been.
  1. Briefly evaluate the validity of this remark by reference to the data, distinguishing intended from unintended investment to the extent possible. What minimum additional information would be required in order to make a rigorous distinction between intended and unintended inventory investment?
  2. Discuss this observation critically in the context of a sensible model of cyclical fluctuations. Do so on the presumption that improved methods of inventory control have lowered the desired inventory-sales ratio.

REMARK: Part A will be given 1/3 weight. Part B will be given 2/3 weight.

1. 1. Consider several alternative growth models which include technical change, labor and capital. What effects would the following policy measures have on growth rates, output/head and consumption /head:
    1. A decrease in the rate of interest;
    2. An increase in the ratio of investment and savings to toal output;
    3. A decrease in the rate of population growth.

________________________

May 17, 1965
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

Part I.

(A) National product is defined as the sum of all final goods each multiplied by its price.
(B) National income is defined as the sum of all net incomes of certain recipients.

Discuss the following questions:

i. What is a final good in (A)? What special problems arise from the presence of certain types of organizations?
ii. What is the rationale of multiplying each product by its price? What assumptions are implied in this procedure? Are they realistic?
iii. Whose net incomes are aggregated in (B)? What assumptions does this procedure imply? Are they realistic?
iv. Could you propose changes or improvements in the above procedures? What additional comments would you like to make?

Explain the following concepts with a particular stress on the assumptions underlying them.
1. The ordinary (Keynes’) multiplier
2. The balanced-budget multiplier
3. The acceleration principle

Indicate the virtues and defects of each concept and their use in economic analysis.

Discuss saving as an economic problem. Trace the treatment of saving before Keynes, by Keynes and after Keynes. Evaluate the contribution of the several authors you mention critically.

Part II

Consider a one-sector economy with:
1. A conventional, constant-returns to scale, diminishing returns, technology
2. A labor force growing at a constant geometric rate
3. No technical progress
4. A ratio of net saving to output which is a falling linear function of the wealth-output (i.e., capital-output) ratio

Trace out the evolution of such an economy under conditions of full employment and full utilization of capacity, starting from an arbitrary stock of capital; and show how its stead-state properties are determined.

“The ‘built-in stabilizers’ cannot stabilize the economy at a full employment level but can dampen oscillations.”

Analyze this statement using the following model:

(1) Y_t = C_t + I_t + G_t Income Definition
(2) C_t = α(Y_t-1 –T_t-1) Consumption Function
(3) I_t = β(Y_t – Y_t-1) Investment Equation
(4) T_t = λC_t Tax Equation

Note: the tax equation is the stabilizer in this model. Assume government outlays G_t are constant through time.

Some economists believe recent high unemployment levels in the United States are structural in nature, others that the main cause has been a fairly simple Keynesian demand deficiency.
1. Explain the main elements of the “structuralist” position. (It will be assumed that you understand Keynesian National Income analysis.)
2. Show how the correct interpretation of these (not mutually exclusive) causes affect the analysis of price level movements in the United States over the past decade, with reference to two or three of the main theories that have been applied.

________________________

September 13, 1965
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

PART I.

“The problem of price flexibility and employment is a silly game based on the inclusion of some debtor-creditor relationships and the exclusion of others.” Comment fully. Why is a special definition of money required here?
“Existing methods of national product computations exaggerate the rate of growth of real product over time in a given country, and overstate the ratio between the real product of highly developed and of underdeveloped countries.” Comment fully and critically.
In the early postwar period it was often said that “Increased production is the best cure against inflation.” Comment fully on this statement. Assume that the increase in output is indeed possible, but indicate what kind of output you have in mind. What other information would you require? In the light of your comments, do you think that a prolonged strike is inflationary or deflationary?

PART II.

According to the 1965 Economic Report of the President:
1. “The general guide for wages is that the percentage increase in total employee compensation per man-hour be equal to the national trend rate of increase in output per man-hour.”
2. “The general guide for prices calls for stable prices in industries enjoying the same productivity growth as the average for the economy; rising prices in industries with smaller than average productivity gains; and declining prices in industries with greater than average productivity gains.” (p. 108)
  1. Using relevant aspects of production theory, what would this policy imply for:
    1. Income distribution
    2. Labor allocation among industries and skills
  2. According to theories of inflation you find most persuasive, what aspects of the price-wage mechanism would be most likely to frustrate the Council guideposts that are outline above?

Your answers should consider departures from competitive behavior where pertinent.

Describe the long term trends in (a) population, (b) output, (c) capital, (d) real wage rates, (e) interest, (f) relative shares, (g) capital-output and other important ratios. What constancies have people claimed to observe? What behavior is explicable by a simple neoclassical model? Which of these regularities seem to require the introduction of technological change or the abandonment of central neoclassical propositions? Mention authors as well as theories.
Discuss the role of (a) floors and ceilings and (b) autonomous investment in theories of growth and fluctuations.

________________________

February 7, 1966
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

Answer three questions, including at least one from each part.

PART I:

Write a comprehensive essay on the subject of “The Distinction between Final and Intermediate Products in economics”.
Include in your essay (but don’t limit yourself to) the following points:
1. The basic philosophy
2. Governmental receipts and expenditures
3. Input-output systems
4. Federal Reserve Index of Industrial Production

Discuss the following aspects of the “Price Flexibility and Employment” problem:
1. The basic statement as presented by Patinkin
2. The role and definition of money
3. The role of expectations
4. Your conclusions
Write a comprehensive essay on the subject of “The Economic Effects of a Redistribution of Income from the Upper to the Lower Income Groups”. Indicate the positions on the subject of several economists whose views are relevant to your essay.

PART II:

Is an economy which has been growing at full employment (and full utilization of capacity) helped or hindered in the maintenance of full employment (and utilization) by a more rapid rate of growth of the labor force?
“I take leave to doubt whether there has ever been a trade cycle, i.e. a self-perpetuating cyclical movement, as opposed to a series of fluctuations due to the propensity of a private enterprise economy to exaggerate its response, either way, to the changes of history as it meets them.” Discuss this remark of Joan Robinson’s.
Consider a conventional one-sector neoclassical growth model (i.e. constant returns to scale and smoothly diminishing returns in labor and capital, full employment). There is no depreciation and the labor supply is growing exponentially. The ratio of investment to output is constant. There is “disembodied” purely labor-augmenting technological progress going on exponentially at the rate a/j where j is the elasticity of output with respect to labor input (not necessarily a Cobb-Douglas constant).

Analyze how the steady-state rate of growth depends on the value of the investment-output ratio.

________________________

May 13, 1966
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

PART I

Beginning at least with Adam Smith, there has been much ado in economic writings about productive and unproductive activities and about their proper treatment in national income and product accounts (and in their subdivisions).
Write a comprehensive essay on this subject. Include in it, but do not limit yourself to, the following points:
1. The principles and procedures followed by the U. S. Department of Commerce
2. Alternative methods which might be followed and the reasons for them
3. Special problems created by the presence of governmental activities
4. The Marxist position on this subject
Write an essay on the subject of “Economic Effects of an Increase in the Stock of Money.” Indicate the position taken by several important economists familiar to you.
Explain the investment criteria which should be used by:
1. A private American enterprise
2. U. S. government
3. A Planning Board of some under-developed country.

Emphasize the differences in criteria to be used and the reasons for the differences.

PART II

A short well-organized answer is best.

Formalize the following assumptions into a model:
1. Current consumption is proportional to last year’s national income;
2. Current investment is proportional to last year’s profits;
3. Current profits are an increasing linear function of current national income and the change in national income since last year;
4. National income is the sum of consumption and investment.

Will the model generate cycles if disturbed, for plausible values of the parameters? (Assume that, other things equal, 40% of a year-to-year increase in national income flows into profits.)

Describe how the response of the model economy would be affected by the imposition of a proportional income tax (with consumption proportional to disposable income).

Same for a proportional profits tax, with investment proportional to after tax profits.

Compare the stabilization effects of the two, if the profits tax is levied so as to raise the same amount of revenue as the income tax at a constant level of national income.

Following is the text of a letter from James Tobin.

“Following is the text of a letter from Joan Robinson:

‘Many thanks for sending me the offprint from Econometrica (Money and Growth). Your Keynesian long-period theory is very different from mine and Kaldor’s. I should say that a lower rate of interest will make the rate of profit higher. The rate of profit r = g/s_p, i.e. is equal to the rate of growth divided by the proportion of profit saved. I should say that, within reason, and provided that an appropriate part of investment is in research and training, a higher rate of investment will generate a higher natural rate of growth, so that deepening need not occur.’

Does this make sense?”

Answer Professor Tobin’s question. (The “rate of interest” refers, say, to the rate on government bonds, the only asset apart from real capital. The “rate of profit” can be taken to be the marginal product of capital in a one-sector economy near a steady state.)

Compare the behavior of output per man or per man-hour in the short-run (i.e. in the course of economic fluctuations) and in the long run, for the economy as a whole. Comment on any analytical issues raised by the behavior.

________________________

February, 1968
GENERAL EXAMINATION IN ECONOMIC THEORY
MACROECONOMICS—TWO HOURS
[Note: recycled exam from February, 1964]

Answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

Part I

Write a comprehensive essay on the subject of “Comparisons of National Income and Product in Time and Space.” Indicate the biases which arise in such comparisons.
“The problem of price flexibility and employment is a silly game based on the inclusion of some debtor-creditor relationships and the exclusion of others.” Comment fully. Indicate what definition of money used in your discussion.
Write a comprehensive essay on the subject of “The Interrelationships between Money, Prices and the Rate of Interest.” Include brief reviews of the relevant theories.

Part II

“In order to prevent a cost-push inflation, wage rates in each firm or industry should not increase faster than its labor productivity.” Comment fully.
“If Hansen is correct, the faster is the rate of growth of population, the lower will be the unemployment level in the U.S.” Discuss fully. Include natural growth of population and immigration. In what respect does the growth of population differ from that of the stock of capital?
Write an essay on “Floors and Ceilings in Business Cycle Theory.” Indicate the specific theories and your methods of testing each.

[handwritten note: “special exam… She received good-/fair+ with charity]

________________________

14.452
FINAL EXAMINATION
May 23, 1968

Please answer each question in a separate examination booklet. Indicate on the front page of each booklet whether you are seeking only a grade in 14.452 or a grade in the general examination in economic theory. Those who seek only a grade in 14.452 should answer two questions in part I and two questions in Part II. Those who are taking the general examination in economic theory should answer two questions in Part II and two in Part III.

Part I

Construct a difference-equation model embodying the following assumptions:
1. Consumption is a linear function of disposable income lagged one time-unit;
2. Tax revenue is proportional to national product;
3. Investment is the sum of a component proportional to the current change in consumption and a component proportional to national product lagged one tie-unit;
4. Imports are proportional to national product lagged one time-unit;
5. Government purchases are constant.

Write down formally the conditions for an oscillatory response of the model to disturbance. When are the oscillations damped? How do variations in the tax rate affect these conditions? Suppose part of government purchases were made negatively proportional to the last observed change in national product?

Why is technical progress an important part of the usual model of economic growth? Could increasing returns to scale play the same role? What is the special role of purely labor-augmenting (i.e. Harrod-neutral) technical progress?
Imagine a planned economy choosing among steady states in the one-sector model, without technical progress. The planner values both consumption per head and capital per head (as a measure of national strength, say) and his preferences can be expressed by a system of conventionally-shaped indifference curves in consumption per head and capital per head.

Use this indifference map and the requirements for a steady state to show how the optimal steady state is chosen. Prove that the optimal capital per head will exceed the “Golden-Rule” (maximal consumption per head) level. Show what happens to the optimal position if the rate of population growth increases. Discuss briefly the case of a one-time upward shift in the production function.

Part II

In the generalized multiplier-accelerator model, the equation $\frac{dK}{dt}=I\left( Y,K \right)$ means that “investment decisions are always carried out”, so that when

$I\left( Y,K \right)\begin{matrix} > \\ < \\ \end{matrix}S\left( Y \right)$

“unintended consumption or saving” occurs. Replace the above equation with $\frac{dK}{dt}=S\left( Y \right)$ and interpret and analyze the resulting model. Compare its behavior with the case analyzed in class.

Suppose I = I(Y,K) and S = S(Y) are the schedules of desired investment and saving. In what sense is I–S a measure of excess demand in the aggregate commodity market?

How is it that no specific supply variables (labor force, for example) appear in this measure? Under what circumstances is it natural to suppose that dY/dt responds to (I–S)? (Y = real output, p = commodity price level). Under what circumstances is it natural to suppose that dp/dt responds to (I–S)?

Consider a one-sector non-monetary model of growth under the following assumptions:
1. The production function in intensive form is q = Ak^b;
2. The wage is equal to the marginal product of labor;
3. Investment demand is such that the after-tax return on capital is always at a target level r*;
4. There is a tax on profits at rate t and the government spends all its revenue on consumption;
5. The savings rates from wages and after-tax profits are both equal to a constant s.

Find the tax rate that will permit a steady state at full employment. When will it be between zero and one? How does it change if s changes? Interpret.

Consider a one-sector growth model, with two factors of production (capital and labor), constant returns to scale, and no technical progress. Suppose that the propensity to save out of profits and capital gains is equal to one, and the propensity to save out of wages and transfer payments (taxes = negative transfers) is zero.

Money, which is non-interest-bearing government debt, is the only alternative asset to capital. The desired money-capital ratio is of the form $\frac{m}{k}=L\left( {f}'\left( k \right)+{{\left( {{\dot{p}}}/{p}\; \right)}^{e}} \right)$ where m is the real per capita stock of money, k is the capital-labor ratio, and ${{\left( {{\dot{p}}}/{p}\; \right)}^{e}}$ is the expected rate of inflation which is equal to the actual rate ${{\dot{p}}}/{p}\;$ in the steady state.

Government purchases are zero and the budget deficit, which is equal to the excess of transfers over taxes, is financed by issuing money.

1. Describe the steady-state characteristics of the model.
2. Find the rate of inflation that maximizes steady-state consumption per head.
3. Suppose that ${{\left( {{\dot{p}}}/{p}\; \right)}_{o}}$ is the rate of inflation in (b) that maximizes steady state consumption per head. Would a higher rate of inflation lead to a higher or lower long-run capital-labor ratio?

Part III

Write a comprehensive essay on the subject of “The Problem of Weights in National Income and Index-Number Construction”.
Explain the criteria which are used, should be used (for what purpose?) and why.
Discuss the economic effects of an increase in the stock of money. Include an evaluation of the positions of several (not less than two) prominent economists familiar to you. How would you test the correctness of their positions?
Discuss the effects of inflation of the level of real investment.

________________________

GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two hours
Sept. 1968

Answer THREE questions, at least ONE from each part. Use a separate examination book for each question.

PART I

“Existing methods of national product computation exaggerate the rate of growth of real product over time in a given country, and overstate the ratio between the real product of highly developed and of underdeveloped countries.”
Comment fully.
Write a comprehensive essay on the subject of “The Interrelationships between Money, Prices and the Rate of Interest.” Include brief reviews of the relevant theories.
Write an essay on the subject of “The Economic Effects of a Redistribution of Income from the Upper to the Lower Income Groups.”
Include in your essay the evaluation of several current theories on the subject.
Consider as many economic effects as you can.

PART II.

“In order to prevent a cost-push inflation, wage rates in each firm or industry should not increase faster than the growth of its labor productivity.”
Comment fully.
Consider the effects of technological progress on employment of labor. Be as comprehensive as you can.
What are the built-in stabilizers and how do they work? Can we rely on them to achieve price stability and full employment?
Discuss the subject fully.

________________________

Spring, 1969
GENERAL EXAMINATION IN MACROECONOMICS
Three Hours

Please answer FOUR QUESTIONS distributed as follows:

Part I—without choice—1 hour
Part II—any two questions—40 minutes each
Part III—any one question—50 minutes

Use a separate examination book for each question.

PART I

The Federal Government wishes to stop the current inflation of the aggregate price level. What are the issues in choosing among various fiscal and monetary policies directed to this end? Try to use macroeconomic models (expressed algebraically, graphically or verbally) to illustrate the problems involved.

PART II

Write an essay indicating what you think are the most important ideas about the determination of the rate of investment in economic theory and in economic practice. (Suppose the problem came up in the course of presenting the static Keynesian macroeconomic model of income determination.)
In the two-asset neo-classical growth model à la Tobin or Sidrauski we have two basic equations:

1. $\dot{k}=sf\left( k \right)-nk-\left( 1-s \right)\left[ \dot{m}+nm+{{\pi }_{m}}m \right]{{p}_{m}}$
2. ${{p}_{m}}m=L\left[ {{p}_{m}}m+k,{{\pi }_{m}},{f}'\left( k \right),f\left( k \right) \right]$

Suppose we add the requirement that

1. ${{\dot{p}}_{m}}=\pi _{m}^{*}{{p}_{m}}$ , that is that the government always vary its deficit to produce a constant rate of deflation $\pi _{m}^{*}$ (which would, of course, be an inflation if .) $\pi _{m}^{*}<0$

1. Show that this model can be expressed by the two equations

1a) $\dot{k}=\frac{sf\left( k \right)-nk-\left( 1-s \right)n\left( {{p}_{m}}m \right)}{\left[ 1+\left( 1-s \right)C \right]}$

where $C={\left[ {{L}_{1}}+{{L}_{3}}{f}''+{{L}_{4}}{f}' \right]}/{\left( 1-{{L}_{1}} \right)}\;>0$

2a) ${{p}_{m}}m=L\left( {{p}_{m}}m+k,{{w}_{m}},{f}'\left( k \right),f\left( k \right) \right)$

Why are the pairs of k and (p_mm) which make $\dot{k}=0$ the same regardless of $\pi _{m}^{*}$ ? HINT: When $\dot{k}=0$ what is the increase in the per capita real money supply? What determines the increase in the total real money supply?

1. Show the dynamics of this system graphically by sketching the combinations of (p_mm) and k that make $\dot{k}=0$ and those that satisfy 2a) (the aa schedule). What is the effect of a higher ${{\pi }_{m}}$ on the stable steady-state stock of capital?
2. Under what conditions can the government force the economy to the golden-rule capital stock by enforcing an appropriate $\pi _{m}^{*}$ through fiscal policy without changing s (assume that p_mm must always be positive for any $\pi _{m}^{*}$ )?

Consider a vintage growth model with fixed factor proportions (clay-clay) a constant labor force (n=0), and Hicks neutral technical change at rate γ. Suppose the economy in question invests every year in a given fixed quantity of new machines (not a constant fraction of income), and has always followed this policy. Assume perfect competition, and full employment.
1. Write down the production function for a given vintage. What rates labor and capital-augmenting technical change are implied?
2. What is the labor requirement per machine of vintage τ?
3. Find the economic life time of capital.
4. Describe the growth paths of output, wages, quasi-rents and the labor share of income.
5. Suppose the economy suddenly doubles its investment and then holds it constant. What will happen to wages and the life-time of capital as time passes?
What growth model or growth model ideas would be helpful in studying the effects of a redistribution of income from businessmen to workers on investment and/or growth? You may develop a model explicitly or simply write an essay reviewing the important concepts and their relevance to the question.

PART III

You are asked to compare the per capita national income of some underdeveloped country, such as Brazil, with that of the United States. Assume that the Brazilian currency (a) is convertible into dollars and (b) that it is not convertible.
Discuss as thoroughly as you can the problems involved in this comparison and the methods used for dealing with them. Evaluate these methods critically and present and justify your own recommendations.
Explain what is meant by “The Money Illusion” and what role does its presence and absence play in theories of employment, interest and prices. Be as comprehensive and as critical as you can.

General Examination Grades in Macroeconomics
Spring 1969

Spring 1969 90 = perfect
[1]	83	Ex+
[2]	79	Ex
[3]	78
[4]	77
[5]	75	Ex-
[6]	75
[7]	75
[8]	74	Ex-/G+
[9]	74	Ex-/G+
[10]	73	G+
[11]	72
[12]	72
[13]	71
[14]	71
[15]	71
[16]	70	G+/G
[17]	70	G+/G
[18]	69	G
[19]	69
[20]	69
[21]	69
[22]	69
[23]	68
[24]	67
[25]	67
[26]	67
[27]	66
[28]	66
[29]	66
[30]	65	G/G-
[31]	65	G/G-
[32]	64	G-
[33]	64
[34]	62
[35]	61
[36]	57	F+
[37]	56	F+
[38]	53	F
[39]	50	?
[40]	49
[41]	48

________________________

MACRO GENERAL
February 3, 1971

DO THREE QUESTIONS, AT LEAST ONE FROM A AND ONE FROM B. 40 Minutes each

A

There has been a long-standing dispute among economists whether money is or is not neutral. Explain what this dispute is about, what the major positions are, and present and justify your own position on the subject.
In order to stimulate investment expenditures by business, President Nixon has suggested a more accelerated treatment of depreciation for income tax purposes. For simplicity assume that every depreciable capital asset can be written off for tax purposes in half the usual time. Analyze the proposal and state and justify your conclusions.
The Bergson Index may be defined as the ratio of Soviet output (industrial production or GNP or a similar measure) to Soviet inputs (labor and capital) divided by a similar ratio for the U.S., first in Soviet and then in American prices for some given year. On finding that this Index is less than one, Bergson has concluded that the Soviet economy is less efficient than the American.
1. Which comparison (that is, in Soviet or in American prices) is more likely to be more favorable for the USSR? Why? (This is the less important part).
2. Evaluate critically Bergson’s conclusions. (This is the more important part).

B

Use a simple macroeconomic model that describes the interaction of the real and financial sectors to describe a theory of determination of the price level. Is simultaneous unemployment and inflation consistent with this theory? What parts of the theory would you modify to take account of simultaneous unemployment and inflation?
Define the “golden rule” growth path and derive conditions for an economy to be on it. Compare some actual economy’s performance to the golden rule and, if you can, estimate the saving necessary to reach it. Would you favor such a policy?
Consumer spending in the U.S. is currently in a slump. What hypotheses can you advance to explain this fact?

________________________

GENERAL EXAMINATION IN MACROECONOMICS
June 24, 1971
TWO HOURS

Please answer THREE questions, at least ONE from each part. Use a separate examination book for each question. Write your CODE NUMBER on your book but not your name.

PART I

In a recent speech, Simon Kuznets suggested the following method for expressing the relative rate of growth of real national income of a country: calculate the relative rate of growth of real income of each person (or family) and then take the unweighted arithmetic mean of these rates. Let us call the resulting rate
1. Compare the rationale behind Kuznets’ suggestion with that of the conventional computation of the rate of growth.
2. For what purposes would you use each method? Why?
3. Suggest other ways for achieving Kuznets’ objective.
4. How would the magnitude of K compare with that of the conventional rate?

(Note: do not worry about the distinction between national income and gross product.)

Write an essay on the subject of “Economic Effects of the Retardation of Population Growth in the U.S.” (You may choose a comprehensive approach or concentrate on some issues you regard particularly important and interesting.
Analyze the effects on aggregate demand and supply, both in the short and in the long run, of a prolonged strike in some important industry. Consider several relevant cases.

PART II

When the current Republican administration came into office it faced substantial and rising rates of inflation, and inherited from the last Democratic administration a moderately restrictive fiscal policy. Write a memo to the President outlining his macroeconomic policy options with pros and cons for each. (Would you list different options if you were Paul Samuelson rather than Milton Friedman?)
Use some complete macroeconomic model to discuss the ways monetary policy influences aggregate demand. Try to judge which mechanisms are likely to be strong and reliable, which weak and uncertain.
Capitalia is a two-class society in which land is not a constraint, workers save and capitalists invest. Its population growth rate is 1%. Nothing has ever happened in Capitalia except exponential growth.
1. What is the rate of return to capital?
2. Does the production function make any difference to your answer in part a)? Explain.
3. If the production function is Cobb-Douglas with capital exponent .2, find the capital per head, output per head, and consumption per head.
4. In an unexpected development, population growth doubles. What begins to happen to the rate of return, per capita saving, and the saving as a fraction of output?
5. The government decides to maintain earlier levels of per capita saving “to avoid the impoverishment of our nation” by taxing workers. Comment on this policy. What will per capita consumption be under this policy?

________________________

Source: Duke University. Rubenstein Library. Evsey Domar Papers, Box 16, Folder “Ph.D. Economic Examinations. Macroeconomics.”

Image Source: “From the Flying Car to the Giant R2-D2: The Greates MIT Hacks of All-Time“, by Robert McMillan. Wired, March 20, 2013.

“Boston’s Harvard Bridge is 364.4 Smoots long. And the fact that anybody would remember this in 2013 was probably the furthest thing from MIT freshman Oliver Smoot’s mind on the October 1958 night that he lay himself down, time and again, along the bridge, allowing his fraternity brothers to measure its length (each Smoot is about 5 feet, 7 inches). It was a fraternity prank, but the next year the bridge’s Smoot markers were repainted. Thus, an MIT landmark — and a unique unit of measurement — was born.

Smoot himself went on to become a board member of the American National Standards Institute — a standards man through and through.”

Tags Domar

Courses Exam Questions Problem Sets Syllabus

MIT. Core Microeconomic theory III. Hal Varian, 1975

Post author By Irwin Collier
Post date 2016-12-09

Hal R. Varian, chief economist at Google since 2007, was a 28 year old assistant professor at M.I.T. in 1975 when he taught my cohort the third in a sequence of four half-term courses that constituted MIT’s required core of graduate microeconomic theory. He assigned draft chapters from his graduate textbook Microeconomic Analysis (published in 1977). For this post I have transcribed the course outline, five problem sets and the final examination for the course.

Core microeconomic theory at MIT in 1974-75:

14.121 (linear models and production) was taught by Martin Weitzman,
14.122 (competitive and noncompetitive market structures) taught by Robert L. Bishop,
14.123 (theory of the consumer and resource allocation) was taught by Hal Varian,
14.124 (capital theory, uncertainty and welfare economics) was taught by Paul Samuelson.

_______________________

14.123—Microeconomic Theory III
Theory of the Consumer and Resource Allocation

Professor Hal R. Varian, E52-353, 3-2662
Spring, 1975

Feb. 5	advanced placement exam
Feb. 10	utility; demand; expenditure
Feb. 12	indirect utility; Slutsky equation
Feb. 17	no class
Feb. 19	no class
Feb. 24	demand functions; duality
Feb. 26	expected utility; properties
Feb. 28	general equilibrium; existence
Mar. 3	welfare theory
Mar. 5	the core of an exchange economy
Mar. 10	general equilibrium and production
Mar. 12	dynamics and general equilibrium
Mar. 17	malfunctions of the market mechanism
Mar. 19	final exam

Course text will be lecture notes available from me. Malinvaud and Arrow and Hahn are highly recommended secondary reading. There will be four or five problem sets and a problem session on Fridays, 9-10:30.

_______________________

14.123 Spring, 1975
Professor Hal R. Varian

Consumer Theory I

Consider a consumer with a Cobb-Douglas utility function:
u(x,y) = a ln x + (1-a) ln y.
Calculate:
1. demand functions for x and y
2. the indirect utility function
3. the expenditure function
4. the Hicksian demand functions.
In a general equilibrium analysis, we cannot take income as an exogenous variable in the demand function since income, y = p^.w, depends on the vector of relative prices. Derive the Slutsky equation for D_pm(p, p^.w) in this case.
At a general equilibrium price vector p*, we have aggregate supply equal aggregate demand:
Σ m_i(p*, p*^.w) = Σ w_i. Show that if all agents have identical marginal propensities to consume each good (D_ym_i(p*, p*^.w) = D_ym_j(p*, p*^.w) for all i and j) then all aggregate demand curves must be downward sloping at equilibrium. More generally, show that D_p(Σ m_i(p*, p*^.w_i)) is negative semi-definite.
Define e_ij= (-p_j/x_i) D_pjm_i(p,y) be the cross price elasticity of good i with respect to price j, and r_i = p_im_i(p, y)/y, the income share of commodity i.
Show that r₁e₁₁ + r₂e₂₁ +r₃e₃₁ = r₁.

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14.123 Spring, 1975
Professor Hal R. Varian

Consumer Theory II

A consumer is found to have a utility function of the form
u = -1/x₁ – 1/x₂.
1. Starting from the utility function, compute the market demand functions for the consumer when he has income y and faces prices p₁ and p₂.
2. Use the market demand functions to show that the indirect utility function is
  u = -( √(p₁) + √(p₂))²/m.
3. Compute the expenditure function from the indirect utility function.
4. Compute the consumer’s compensated and market demand curves from the expenditure function.
Suppose at prices (p₁, p₂) = (5,10) and income y = $100, a rational consumer consumes the bundle (6,7). Assume that we have measured the following derivatives:

∂H₁/∂p₁(p₁, p₂, ū) = -2
∂H₁/∂p₂(p₁, p₂, ū) = +1
∂M₁/∂y (p₁, p₂, y) = 2/7

where H₁ and H₂ are the Hicksian demand functions for goods 1 and 2 and M₁ is the Marshallian demand function for good 1. Find an estimate of the consumption bundle of the consumer at (p₁, p₂) = 5,11).

Suppose a consumer has an expenditure function of the form e(p, u) = u^.g(p). Show that his utility function is homogenous of degree one. Suppose e(p,u) is of the form e(p,u) = h(u)g(p). How does the consumer’s behavior differ?
Suppose a consumer has a differentiable expected utility function for income with D_yu(y) strictly positive. Show that he will always take a small enough bet as long as it has positive expected value.

_______________________

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium III

Show that Walras law holds for a production economy with fully distributed profits.
Prove the theorem that a general equilibrium is pareto efficient for an economy with production.
Suppose we have a productive economy with two agents. The producer has a production function x = q^1/2 where x is output and q is labor.
The consumer has a utility function u(x,q) = x^1/2(1-q)^1/2. Calculate the general equilibrium real wage and equilibrium level of profits.

_______________________

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium Theory and Welfare Economics I

Show that any solution to

max Σ a_iu_i(x_i), a_i>0
s.t. Σ x_i ≤ w

is necessarily pareto efficient.

Suppose we have two agents with indirect utility functions

v₁(p₁, p₂, y) = ln y –a ln p₁ – (1-a) ln p₂
v₂(p₁, p₂, y) = ln y –b ln p₁ – (1-b) ln p₂

and initial endowments

w₁ = (1,1)
w₂ = (1,1)

Calculate the market clearing price.

We have two agents with utility functions

u₁(x₁, y₁) = a ln x₁ +(1-a) ln y₁u₂(x₂, y₂) = b ln x₂ + (1-b) ln y₂

and initial endowments

w₁ = (1,0)
w₂ = (0,1)

Calculate the market equilibrium prices in terms of the parameters a and b.

_______________________

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium Theory and Welfare Economics II

Two agents with strictly convex preferences have equal initial endowments
w₁ = w₂. They trade to an arbitrary allocation in the Core (w₁,w₂), (x₁,x₂). Prove that this allocation is necessarily fair:
1. Draw an Edgeworth box and give a geometric argument;
2. give an algebraic argument in the general case (there is a one-line proof.)
3. Show in a three person economy there are allocations in the equal division core that are not fair.
Suppose we have n agents with identical, strictly convex preferences and we have some initial bundle of k goods to be divided among them. Let x be a fair allocation; show that x must give the same bundle to each agent. (Recall that a fair allocation is one that is strongly pareto efficient and such that no agent prefers any other agent’s bundle to his own.)
Show that under appropriate assumptions of convexity, every pareto efficient allocation is necessarily a solution to a problem of maximizing a weighted sum of utilities. What is the economic interpretation of the weights?
Suppose we are at a market allocation that is considered good. Since it is a market equilibrium it is pareto efficient and therefore maximizes a certain weighted sum of utilities Σ a_i* u_i(x). Accordingly, we will use Σ a_i* u_i(x) to evaluate small projects. Suppose we are considering a small project that will change x = (x₁,…, x_n) to x´= (x₁´,…, x_n´). Show that it should be undertaken if and only if it increases national income; that is, iff Σ p^.(x_i´-x_i) >0.

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14.123 FINAL EXAMINATION
March 19, 1975

Professor H. Varian

Answer any 2 out of 4. All questions have equal weight. Good luck!

A consumer has a utility function of the form u(x₁, x₂) = ln x₁ + x₂. He faces prices p₁ and p₂ and has income y. Calculate:
1. his Marshallian demand functions for each good
2. his indirect utility function
3. his Hicksian demand functions
4. his expenditure function.
There are two consumers A and B with the following utility functions and endowments:

U_A(X_A¹, X_A²) = a ln X_A¹ + (1-a) ln X_A² , W_A = (0,1)
U_B(X_B¹, X_B²) = min (X_B¹, X_B²) , W_B =(1,0)

Calculate the market clearing prices and the equilibrium allocation.

We have n agents with identical strictly concave utility functions, u₁(x₁),…,u_n(x_n). There is some initial bundle of goods w. Show that equal division is a pareto efficient allocation.
A consumer has a differentiable expected utility function u(y) with u´(y) > 0. (There are no conditions on u´´(y)). His initial level of wealth is w and he is contemplating a bet which gives him $e with probability p > ½ and he loses $e with probability 1-p. (Notice the bet has positive expected value.) Show that he will always take the bet if e is small enough. (Hint: try Taylor series.)

Source: Personal copies.

Image Source: Detail from 1976 departmental group photo.

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Exam Questions M.I.T.

MIT. Microeconomic Core Theory II. Bishop, 1974

Post author By Irwin Collier
Post date 2016-12-08

_______________________________

“Microeconomic Theory II”, the second of four half-semester core microeconomic theory courses at MIT, was actually the first offered during the academic year 1974-75. It was taught by Professor Robert L. Bishop. In this post we find 29 sample questions for the five sets of topics covered in the courses. Also included are the waiver exam for testing out of the course and the final examination for the students who took the course

The course “text” was the mimeographed manuscript on economic theory written by Bishop that was on closed reserve at Dewey Library and consulted by presumably at least a dozen cohorts over the 1960s (perhaps even earlier) and 1970s. A copy of that manuscript can be found in the Edwin Burmeister papers at Rubenstein Library of Duke University.

Two papers (especially the second) by Bishop covering some of the course material are:

Bishop, Robert L. “Duopoly: Collusion or Warfare?” The American Economic Review 50, no. 5 (1960): 933-61.

Bishop, Robert L. “The Effects of Specific and Ad Valorem Taxes.” The Quarterly Journal of Economics 82, no. 2 (1968): 198-218.

Core microeconomic theory at MIT in 1974-75:

14.121 (linear models) was taught by Martin Weitzman,
14.123 (duality) was taught by Hal Varian,
14.124 (capital theory, uncertainty and welfare economics) was taught by Paul Samuelson.

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Topics in 14.122, with Sample Questions

Review of demand and supply, elasticities. Walrasian v. Marshallian stability conditions. Demand and supply as seen by the individual seller or buyer.
1. What various formulas have been proposed for measuring the arc elasticity between two points on a demand curve, (q₁,p₁) and (q₂,p₂)? Discuss the virtues and defects of the various definitions. Can any one be said to be “best”?
2. Compare the Walrasian and Marshallian stability conditions as to (a) their content, (b) the types of markets in which they are realistically applicable, and (c) the situations in which they do not agree.
3. If 1000 sellers have fixed supplies of 50 units each of a good, how does the demand confronting each individual seller relate to the market demand (a) as to slope, (b) as to elasticity? How are the answers affected if each seller has a positively sloped supply schedule?
Review of the revenue and cost curves of the firm and its long-run and short-run equilibrium. Comparative implications of competitive and monopolistic equilibrium.
1. Show how the price elasticity of demand for a good is related to average and marginal revenue. Why is a monopolist never in static equilibrium in the range where his demand is relatively inelastic?
2. Given the linear demand p = a –bq, show that price elasticity depends only on p and a, or only on q and a/b. When do two linear demands have the same elasticity (a) at any given price, (b) at any given quantity?
3. Given two linear demand (with different slope and different axis-intercepts) and a point on one of them, find geometrically the point on the other with the same elasticity.
4. A linear demand and a demand that is concave from above are tangent at a particular point. In the vicinity of that output, how much can you say about the relative magnitudes, slopes , and curvatures of the respective marginal revenue curves?
5. Given relevant segments of a monopolist’s AR, MR, and MC curves (but not AC), show how much his profit is reduced if he is forced to charge a somewhat lower price than his profit-maximizing one—on the assumption that he still has an incentive to satisfy the full demand at the new price.
6. “Short-run marginal cost is typically smaller than long-run marginal cost, since the former reflects only variable cost while the latter reflects full cost.” Discuss.
7. Discuss the virtues and limitations of Lerner’s concept of the degree of monopoly power, M = (AR-MC)/AR. Would it make any difference if he had defined it as M´ = (AR-MR)/AR?
8. “A profit-maximizing monopolist, in contrast to a pure competitor, would always prefer to sell more than he actually can, at the price he hooses to set. This is why monopolists frequently advertise and pure competitors never do; and it is also why equilibrium can be analyzed by means of demand and supply curves in pure competition but not in monopoly.” Discuss.

Long-run and short-run equilibrium of the purely competitive industry, with comparative statics problems. Supply curves reflecting pecuniary v. real or technological externalities.
1. Give as many distinct reasons as you can why a purely competitive industry’s long-run supply curve may be positively sloped? Negatively sloped?
2. “If a purely competitive industry’s long-run equilibrium is disturbed by a sudden increase in demand, the effects on price are likely to be greater in the short run than the long, and the effects on output are likely to be just the opposite.” Discuss.
3. Under what circumstances, if any, is the Marshallian producers’-surplus area above a supply curve a defensible concept? When is it clearly indefensible?
4. In a purely competitive industry with negatively sloped demand, can a commodity tax lower the price? Can it raise price by more than the amount of the tax? Show that the answers differ according as the stability conditions are assumed to be Walrasian or Marshallian.
5. In a purely competitive industry where firms all have u-shaped costs and the industry’s long-run supply is horizontal, compare the effects of a specific commodity tax, a franchise tax, and a limited licensing of firms—such that all would have the same effect on industry output.
6. Assume that a distinctive type of grape can be grown only on a distinctive type of vineyard land, which is valueless in any other use. This land varies widely in quality from one acre to another. The only other factor, labor, is homogeneous and in perfectly elastic supply to this single industry. (Assume, for convenience, that one firm always cultivates just one acre, irrespective of relative factor prices.)
  1. If the land is widely owned and the grape industry is purely competitive, show how its long-run supply curve is derived. Then, for some given grape demand, show how the aggregate equilibrium rent is determined.
  2. What would be the comparative effects of a tax on the grapes and a tax on the vineyard land that would raise the same revenue? Might the landlords ever prefer the latter tax?
  3. Starting from the equilibrium in (a), assume that laborers become free to allocate themselves on the vineyard land and receive equal per capita shares of the total grape revenue. How would this affect the price and quantity of grapes, incomes, and allocational efficiency?
7. Explain why, in some purely competitive industries, social marginal cost may be different from private marginal cost.
Comparative statics of monopoly: changes of demand, cost, taxes, various regulations. Equilibrium with advertising, with price discrimination, with systematic seasonal shifts of demand.
1. In a monopoly with negatively sloped demand, can a specific tax lower price? Can it raise price by more than the amount of the tax? Show that the answers depend on the second-order conditions for a profit maximum. Are these special results more or less likely than in pure competition (cf. question 15).
2. For any given specific tax, does a fully equivalent ad valorem tax exist (a) in pure competition, (b) in monopoly?
3. “Not only does a monopolized industry produce less than a competitive one would, but also when superior productive equipment becomes available, the monopolist is motivated to introduce it more slowly.” Explain wherein you agree or disagree.
4. What determines whether a static-equilibrium monopoly price will rise or fall in response to an increase of demand? Does it make any difference whether the demand increase is spontaneous or induced by advertising? Can an increase in demand ever reduce a monopolist’s equilibrium output?
5. Under what circumstances will a price ceiling imposed on a monopolist
  1. leave him with incentive to satisfy the full demand at that price,
  2. induce him to produce an output that is positive but not great enough to satisfy the full demand, or
  3. drive him out of business?
6. “The greater is a firm’s degree of monopoly power (in Lerner’s sense), the more likely is it to find advertising profitable.” What can be said for and against this proposition?
7. When is it profitable to discriminate as to price in two markets for a physically homogeneous product? Are there any circumstances in which the buyers in both markets may benefit from the discrimination?
Monopolistic competition: oligopoly and product differentiation.
1. Why are none of the duopoly solutions proposed by Cournot, Bertrand, Stackelberg, and Chamberlin wholly satisfactory?
2. If duopolists produce differentiated products, what are the comparative consequences under (a) price-quoting and (b) quantity-setting? Specifically, compare the Cournot and Bertrand equilibria, the corresponding Stackelberg equilibria (and warfares), the potentialities for collusion, and the potentialities for warfare.
3. How and why is the problem of oligopolistic interdependence allegedly avoided in Chamberlin’s large-group case of monopolistic competition? Are you satisfied that it is really avoided? Compare it in this respect with pure competition.
4. As compared with simple monopoly, what additional sources of uncertainty are there with respect to comparative-statics problems under monopolistic competition?

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Waiver Exam—14.122
September 11, 1974

Answer any TWO questions (about 40 minutes each):

Question 1:

Show how the total, average, and marginal cost curves of a one-product firm are related to one another in the long-run—as to intersections, minima, inflection points, etc. (Assume that the total-cost function is continuous up to at least its second derivative and that production is subject first to net economies of scale and then to net diseconomies.)
Show how those same long-run cost curves are related to their short-run counterparts, identifying all notable points of correspondence.

Question 2:

In a small community surrounding a lake, workers can get all the employment they need in industry at a wage of $20 per day. An alternative employment is to catch fish in the lake and sell it in the environs at a constant price of $10 per bushel. With labor valued at the going wage, the cost of fish per bushel rises with the total amount of fishing. Specifically, the average cost of fish (in dollars per bushel) is related thus to the total number of bushels caught per day:

C = 2 + .005q

With free entry to the lake, how much fish will be caught?
Show that everybody can be made better off if the community levies an appropriate tax per bushel of fish. What is the optimal tax?
If, alternatively, the lake were privately owned and the owner could hire labor to catch fish at the same cost as before, what output would maximize his net income?
Would it always be appropriate, as in (b), to impose a tax on any competitive industry with a positively sloped supply curve? Explain briefly.

Question 3:

“If a specific tax of given magnitude is imposed on a good that is producible at constant unit cost, the equilibrium price may be raised either more or less under monopoly than under competition. Even when the price rises by an appreciably smaller amount under monopoly, however, it is still very likely to be socially disadvantageous to tax such a monopolized good rather than competitive ones.” Explain fully wherein you agree or disagree with each sentence.

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14.122
November 1, 1974

One hour and a half
Answer any FIVE of the following six questions:

If a specific tax is imposed on a commodity produced by a purely competitive industry, what effects on price can be ruled out under the stability conditions specified by (a) Marshall; (b) Walras? Explain.
You are given this cost function:

C= aq_c+ bq,

where C is total cost, q_c is an absolute-capacity output (fixed in the short run), q is the actual output (less than or equal to q_c), and a and b are positive constants. Draw carefully the implied long-run cost schedules and several sample sets of short-run cost schedules—total, average and marginal. Comment on the relationship between long-run and short-run marginal cost.

“When the demand for a monopolist’s product increases, his profit-maximizing price may rise, remain the same, or fall. The conditions governing this result are exactly the same whether the increase in demand is spontaneous or induced by advertising.” Explain why you agree or disagree.
“Fully equivalent specific and ad valorem taxes are possible in pure competition but not in monopoly.” Explain why you agree or disagree.
When does a positively sloped supply curve imply some form of producers’ surplus, and when does it not? Explain.
In an oligopoly with differentiated products, would the price be lower in a Cournot equilibrium or a Bertrand equilibrium? Explain.

Source: Personal copies.

Image Source:Robert L. Bishop at MIT Museum .

Tags Bishop

Courses Exam Questions M.I.T. Suggested Reading Syllabus

M.I.T. Capital Theory, Uncertainty, Welfare Economics. Half-semester Core Microeconomics. Samuelson, 1975

Post author By Irwin Collier
Post date 2016-12-07

From my files from graduate school I have transcribed the syllabus and final exam for the fourth of the four half-semester core microeconomic theory courses taught at M.I.T. during the academic year 1974-75. The topics of capital theory, uncertainty and welfare economics fell to Paul Samuelson. The preceding three half-semester microeconomics theory courses were taught by Robert Bishop, Martin Weitzman and Hal Varian.

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READING LIST FOR 14.124
P. A. Samuelson
SPRING 1975

MICROECONOMIC THEORY

I. CAPITAL THEORY

I. Fisher

Theory of Interest
Part II, all; Part I, Chs. 1,3; Part III, Chs. 10,11.

E. Böhm-Bawerk

Positive Theory of Capital
Book V, all; Book VI, Chs. 6,7,8.

R. M. Solow

“A Contribution to the Theory of Economic Growth”
Quarterly Journal of Economics, February, 1956; pp. 65-94.

Capital Theory and the Rate of Return
(DeVries Lectures) North-Holland, Amsterdam, 1963.

T. Koopmans

Three Essays, pp. 105-126.

F. Ramsey

E.J., 1928

N. Kaldor

“Alternative Theories of Distribution”
RES, 1955

Sraffa

Production of Commodities by Means of Commodities
Chs. 1, 2, 3.

Dorfman-Samuelson-Solow

Linear Programming and Economic Analysis
Chs. 11, 12.

A. Samuelson

“A Summing Up”
QJE, 1966

II. ECONOMICS OF UNCERTAINTY

K. Arrow

Theory of Risk Bearing
Chs. 3,1,2,4.

J. Tobin

RES, 1958

H. Markowitz

Portfolio Selection
sample

III. MODERN WELFARE ECONOMICS

A. Bergson [A. Burk]

“A Reformulation of Certain Aspects of Welfare Economics”
QJE, 52 (February 1938)
pp. 310-334

J. Hicks

“The Foundations of Welfare Economics”
EJ, 49 (December 1939)
pp. 696-712

P. A. Samuelson

Foundations of Economic Analysis (Harvard University Press, Cambridge, Mass., 1947)
Chapter 8, “Welfare Economics”

P. A. Samuelson

“The Pure Theory of Public Expenditure”
Review of Economics and Statistics, 36 (November 1954)
pp. 387-389

reproduced as
Chapter 92
The Collected Scientific Papers of Paul A. Samuelson, Vol. II
MIT Press, Cambridge, Mass., 1966; editor: J.E. Stiglitz

K. Arrow

Social Choice and Individual Values, 1951
Cowles Foundation for Research in Economics, Monograph #12
Wiley, New York, second edition, 1963

J. Rawls

A Theory of Justice
Harvard University Press, Cambridge, Mass., 1971

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Background Reading

A. C. Pigou

The Economics of Welfare, 1920
Macmillan, London, 4^th edition, 1932
reprinted in new appendices, 1952

L. Robbins

An Essay of the Nature and Significance of Economic Science, 1932
Macmillan, London, 2^nd edition, 1935

van der Graaf

Theoretical Welfare Economics
Cambridge University Press, London, 1957, paperback

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FINAL EXAM
14.124
MAY 20, 1975

This is a 1 ½ hour exam. You may take up to an extra half hour, but only if you need it and not in order to establish extra credit for all you know.
Answer any 3 of the following four questions, thus allowing about one half hour for each.

Society consists of 2N people [equal numbers of men (i=1) and women (i=2)] who will live and consume for two periods: t=1,2, or now and tomorrow. Also, society has a Solow neoclassical production function:

C(t) + K(t+1) = F[L(t),K(t)]

All 2N people have the same labor, namely L_i(t) = 1/2N. The women or men possesss equal shares in the initial capital good, K(1) = k/2N, but it is an unknown of the problem to find out what will be K(2).

Intertemporal tastes of the representative man and woman involve the same concave u[C(t)] function, and with equal Böhm-Fisher subjective time preference factors, ρ₁ and ρ₂, in:

U₁ = u[C₁(1)] + u[(C₁(2)]/(1+ρ₁), U₂ = u[C₂(1)] + u[(C₂(2)]/(1+ρ₂), ρ₁ = ρ₂.

(You may set N=1 to simplify your expositions if you wish to do so.)
The equilibrium is now determinable.

(a) Describe graphically, and/or mathematically, and/or literally, how Irving Fisher or any modern economist would determine the equilibrium for:

C₁(1)*, C₁(2)*, C₂(1)*, C₂(2)*, K(2)*; r*, the rate of interest between period 1 and 2. (Hint: Will women lend to men or borrow from them?)

(b) Very briefly, modify your above answer to show what will happen when men are more “impatient” than women, so that ρ₁ > ρ₂.

Prove that fair-game investing or gambling will (a) be avoided by what class of people?; (b) be embraced by what class of people? How do you reconcile under (a) the purchases of insurance at unfavorable-game premiums?

Lerner, Lange, and others wish to utilize market pricing in achieving maximization of a social welfare function appropriate to a socialist state where (a) all non-labor inputs are owned by the State; (b) “people’s changing tastes are to count,” (c) where the bureaucrats responsible for the different industries do not necessarily in every case face constant returns to scale and classical returns.

Describe how goods and services should be priced, how people’s total spendable incomes are to be determined, and also any special problems that might arise for the Lerner-Lange-Smith VISIBLE HAND.

Bentham says that people may differ in the heights of their marginal utility from the same number of chocolates (or real incomes). But he believes that this difference in intensities of enjoyments is distributed “in about the same way among the very rich and the very poor.” What kind of income tax formula would he then presumably want to legislate? What “incentive effects” would you want to keep in mind appraising this solution?

Source: Personal copies

Image Source: Left to right: Robert C. Merton, Jerome Bert Wiesner and Paul A. Samuelson with Vol. 3 of Samuelson’s Collected Scientific Papers (1972). MIT Webmuseum.

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Chicago Economists Exam Questions

Chicago. Price and Distribution Theory. Taught by Viner and attended by Samuelson, 1935.

Post author By Irwin Collier
Post date 2016-11-24

The graduate economics course at the University of Chicago “Price and Distribution Theory” as taught by Jacob Viner was often referred to by Paul Samuelson. From the Paul A. Samuelson papers at Duke University we have a copy of the examination questions for that course together with a copy of Jacob Viner’s evaluation of his “with one possible exception, the most promising undergraduate I have ever encountered since I began teaching some twenty years ago”. Any clues as to who might have claimed the status of the “one possible exception”? Viner’s cover note to Samuelson and the latter’s gracious response are included for the sake of completeness.

I have already posted the reading list for the 1932 vintage of the course.

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Course Description

[Economics] 301. Price and Distribution Theory.—A study of the general body of economic thought which centers about the theory of value and distribution and is regarded as “orthodox theory,” including the critical examination of some modern systems of this character. Prerequisite: Economics 209 or its equivalent and the Bachelor’s degree. Summer, 9:00 Knight; Winter, 10:00, Viner.

Source: Announcements. The University of Chicago. The College and the Divisions for the Sessions of 1934-35, p. 286. (Note the 1936-37 course description Announcements is identical to that of 1934-35, so we can assume the course announcement in the 1935-36 Announcements would too.)

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[Samuelson’s handwritten note and the copy of the 1935 examination for Economics 301]

My Final Exam for Viner’s famous course. Only 3(a) caused me trouble (no wonder!)
PAS 6/30/72

Examination in Economics 301
Winter Quarter, 1935-

Discuss the relationship of marginal cost to prices:
1. under short-run competitive equilibrium;
2. under long-run competitive equilibrium

when (1) the industry is subject to external diseconomies of large production; (2) the industry operates under conditions of constant cost.

In order that an industry shall operate at constant costs as its output is varied, what conditions must hold as to:
1. the definition of “industry”;
2. the supply curves, general and partial, of the factors used by that industry;
3. the mode of operation of the law of diminishing returns in that industry;
4. the presence or absence of internal diseconomies of large-scale firms in that industry;
5. the size of the changes in output?
Comment briefly on the following statements:
1. “If labor has effective occupational mobility, the prices of all commodities under competitive conditions will tend to equal their marginal labor costs.”
2. “Labor is paid out of current product, and if advances are made, they are made by laborer to employer, rather than vice versa.”
3. “Saving is necessary only in an expanding economy. No one need wait for the product of his labor or property in a stationary economy.”
4. “Any increase in investment lengthens the production period, and the production period cannot be lengthened unless more investment takes place.”

___________________________________

Jacob Viner’s Handwritten Note to Paul Samuelson, 1963

Jacob Viner
13 Newlin Road
Princeton, New Jersey

Aug. 7, 1963

Dear Paul,

I have just run across my carbon copy of a 1935 appraisal of you by me and am sending you a reproduction of it not to raise your ego but to raise mine. I recall your report at Pittsburg of a less perspicacious appraisal of about the same period by Paul Douglas. In this instance at least I showed skill apparently as a forecaster.

Cordially yours,
Jack

___________________________________

Jacob Viner’s Recommendation for Paul Samuelson to SSRC, 1935

The Social Science Research Council
230 Park Avenue
New York City

Mr. Paul A. Samuelson, although an undergraduate, did distinctly better work than any other member of my graduate course in Economic Theory during the past Quarter. He is a sober, careful and extremely able student, equipped with extensive mathematical technique, zealous, original and independent, without the belligerence and the arrogance that so often marks young men with keen minds and the knowledge that they are superior in mental capacity to their classmates. Mr. Samuelson shows all the signs of having it in him to become a very distinguished economic theorist, and is, with one possible exception, the most promising undergraduate I have ever encountered since I began teaching some twenty years ago. I have only known him for some four months, but I do not think that this is a too hasty judgment.

Jacob Viner
Professor of Economics
Chicago, Illinois

April 15, 1935
University of Chicago

___________________________________

Paul Samuelson’s response to Jacob Viner, 1963
Carbon copy

August 23, 1963

Dear Jack:

I had to be flattered by your August 19 note and the enclosed carbon of your 1935 evaluation of me. I feel as proud of that young man as if he had been my son and prouder still after your early discernment of his “growth-stock” potential.

Your 1935 graduate course certainly stimulated me. It sent me to Harvard well-prepared—over-prepared some of my teachers may have thought!

Last June I basked in the reflected glory of your Harvard degree.

Our love to Frances,

___________________________________

Source: Duke University. Rubenstein Library. Paul A. Samuelson Papers, Box 74, Folder “Viner, Jacob (corresp) 1935-1990”.

Image Source: University of Chicago Photographic Archive, apf1-08490, Special Collections Research Center, University of Chicago Library.

Tags Douglas, Samuelson, Viner

Columbia Economists Exam Questions History of Economics

Columbia. Classical Economics Exam by J.M. Clark. 1951

Post author By Irwin Collier
Post date 2016-10-14

John Maurice Clark taught a history of economic theory sequence at Columbia University that had its origins in a similar course that had been taught earlier by Wesley Clair Mitchell. On the back of Clark’s examination questions for the first session of the 1950-51 academic year one finds a list of names and grades that we can strongly presume constitute the grade distribution for the course. 43 students were listed by John Maurice Clark in his handwritten grade sheet for the first semester of formative types of economic theory, of whom 26 received grades (3.12 average on a 4 point scale, median 3.17). Mark Blaug, whose magnum opus Economic Theory in Retrospect has served as a staple of the analytic narrative of the evolution of economics, received only a grade of B- (2.67) which put him tied with two other students at rank 21. A few years later Blaug was to find his mentor and dissertation adviser, George Stigler.

The later Congressional Research Service economist John P. Hardt (Columbia Ph.D., 1954) was on the list but not awarded a grade for the course.

Oops it happens every so often, I have repeated myself. The original posting along with another year’s examination can be found here.

_____________________

Course Announcement

Economics 115-116 — Formative types of economic theory.
3 points each session. Professor Clark.
M. W. 12. 313 Fayerweather.

Readings and critical discussion of outstanding examples of the parent stock of classical economics with some regard to historical setting, and of subsequent outstanding contributions.

Source: Columbia University. Announcement of the Faculty of Political Science for the Winter and Spring Sessions 1950-51, p. 46.

_______________________________

Course Description

Economics 115-116—Formative types of economic theory. 3 points each session. Professor Clark.

M.W. 12. 313 Fayerweather.

Readings and critical discussion of outstanding examples of the parent stock of classical economics, with some regard to historical setting, and of subsequent outstanding contributions.

Source: Columbia University. Announcement of the Faculty of Political Science for the Winter and Spring Sessions 1950-51, p. 46.

_______________________________

Take-Home Examination Questions

Economics 115
Final Examination
January, 1951

Answer any two questions, taking about the time for the actual writing that a regular examination would take. Those who do the work during Christmas holidays will please return papers January 8; others Friday, January 26, unless otherwise specified.

Do the views of ancient writers (Hebrew, Greek or Roman) afford the same kind of evidence as the writings of modern economists as to economic conditions and practices of their time?
Discuss extent of applicability of medieval doctrine on price; variations or relaxations; and how far the doctrine was effective in practice.
Explain and appraise Quesnay’s “Tableau Économique”.
State key doctrines of the Physiocrats and indicate how they could be regarded as adaptations to an historical situation.
Compare views of Smith and Ricardo on the relation of labor to value.
Compare treatment of rent in Smith, Malthus and Ricardo.
On what grounds did Adam Smith sanction departures from laissez-faire?
Topic: dominant conceptions of what economic activity is for. Compare the dominant conception (or at most a few dominant conceptions) of as many of the following as you feel you can reasonably cover: typical Mercantilists, Physiocrats, Ricardo, John Stuart Mill.
What does Bentham’s theory contribute to the basic rationale of economics, aside from his ideas on economic matters themselves? (Book V of J. S. Mill’s “Principles of Political Economy” might contain hints.)
State doctrines of Ricardo which had roots in historical conditions of the time, and indicate the connection.
Compare Ricardo’s treatment of value with either Adam Smith’s or John Stuart Mill’s.
What were the sources of J. S. Mill’s departure from strict Ricardianism?

_______________________________

Probable Grade Distribution

Letter Grade	Number of students
A	2
A to A-	1
A-	5
B+	5
B	6
B to B-	1
B-	2
C+	1
C	3

Note: Mark Blaug received the B to B- grade.

Source: Columbia University Archives. John M. Clark Papers. Box 24 (Courses Misc.), Unlabeled Folder.

Image Source: Portrait of John Maurice Clark from the collection of portraits of economists presented in 1997 as a gift to the Department of Economics of Duke University by Professor Warren J. Samuels of Michigan State University. Free use of these portraits in Web documents, and for other educational purposes, is encouraged: users are requested to acknowledge that the images come from The Warren J. Samuels Portrait Collection at Duke University.

Tags Blaug, ClarkJM

Courses Exam Questions Toronto

Toronto. Honors Exam. Money, Credit and Prices. 1933

Post author By Irwin Collier
Post date 2016-09-28

_______________________________

The honors examination questions for Money, Credit and Prices from the University of Toronto transcribed below were filed away by A. G. Hart in a folder marked “Chi[cago] Qualifying”, perhaps not an ideal resting place for this particular archival artifact. At least now these exam questions are discoverable through a standard internet search and provide researchers going to the University of Toronto archives a tip should they search for economics course materials there.

_______________________________

Course descriptions

3e. Money, Credit and Prices. A course dealing with monetary theory and related subjects, including the discussion of the role of money in economic theory; bimetallism; the gold standard; the gold exchange standard; the relation between money, credit, production and prices; the business cycle; central banks and the control of credit; stabilization of business; the foreign exchanges; the role of money in the theory of international trade; money and foreign exchange; problems in various countries, including reparations. For reference: Cassel, Theory of Social Economy, Vol. II, and Money and Foreign Exchange after 1914; Fisher, The Purchasing Power of Money; Keynes, A Treatise on Money; Marshall, Money, Credit and Commerce; Edie, Money, Bank Credit and Prices; Willis and Beckhart, Foreign Banking Systems; Burgess, Interpretations of the Federal Reserve Bank; Mitchell, Business Cycles, the Problem, and its Setting; Snyder, Business Cycles and Business Measurements; Hobson, Rationalization and Unemployment; Gregory, Foreign Exchange; Taussig, International Trade; Angell, International Prices; The Young Plan; Reports of Agent General for Reparations; Reports of League of Nations Gold Delegation; The Macmillan Report, 1931; Current Financial Literature. Three hours a week.

3h. Banking. A special course on the theory and practice of banking operations. One hour a week.

Source: University of Toronto Calendar, Faculty of Arts 1932-33. University of Toronto Press, pp. 112-113.

Image Source: Detail from photo of A. F. Wynne Plumptre (1972) from the University of Toronto Archives Image Bank.

_______________________________

Card paper clipped to examination copy

I thought you might find this of interest.
A. F. Wynne Plumptre [B.A., Lecturer]
Kings College, Cambridge
Toronto, Canada

_______________________________

UNIVERSITY OF TORONTO
FACULTY OF ARTS

ANNUAL EXAMINATIONS, 1933

THIRD YEAR—HONOUR

ECONOMICS 3e, 3h
MONEY, CREDIT AND PRICES

Examiners—The Staff in Economics

(Question ONE must be answered by all candidates, and THREE or FOUR other questions.)

What do you mean by “inflation”? Under what circumstances, if any, is it desirable?
The following figures appear in the monthly returns of the combined Canadian Chartered Banks:

(in millions of dollars)

	Sept. 1929.	Sept. 1932.
Current Commercial loans	1,404	1,003
Total Securities held	487	704
Demand Deposits	759	481
Notice Deposits	1,471	1,359
Bank Notes in circulation	197	132
Finance Act borrowings	79	23

Sketch the probable causes of these movements.

It is said, often in criticism of French financial methods, that the power of finance is used in that country to further political ends. In England, on the other hand, efforts have usually been made to keep “politics” dissociated from “finance”; i.e., to keep politicians from dictating the country’s monetary and financial policies. How far, in your opinion, can or should the two be kept separate in Canada or any other country?
“The establishment of the federal reserve bank system…is actually the reason why they have had the recent trouble in the United States banks.” (Sir John Aird, quoted in the Toronto Daily Star, March 22^nd, 1933.) How far do you agree with this statement?
In maintaining the gold standard, “world wide international co-operation becomes all but essential just at the moment when the particular local manifestations of the universal trouble occupy the whole attention of the Government in each country and make international action specially difficult.” (Sir Basil Blackett.) Is this a fair summary of the causes of the breakdown of the international gold standard? If so, does it necessarily follow that the restoration and subsequent maintenance of the gold standard is impracticable?
Give an outline of what is meant by any two of the following policies:

Bimetallism,
Remonetization of silver,
Revaluation of gold,
Reduction of central bank reserve ratios.

Outline very briefly the theory of “comparative costs” in international trade. How far do you think it is desirable that members of the newly appointed Canadian tariff board should be familiar with the principles of this theory?
Do you believe that monetary policy is, or might be, a major factor in determining the level of prices and prosperity in either Canada or England or some other country? (Candidates should answer this question with respect to one country only.)
“Booms and slumps are simply the expression of the results of an oscillation of the rate of interest about its equilibrium position.” (J. M. Keynes.) How far do you agree?
Suppose that, at the forthcoming World Economic Conference, it were generally agreed that international exchange rates should be stabilized immediately. What factors would you then take into consideration in estimating at what rate the Canadian dollar should be stabilized? How far would the theory of “purchasing power parity” assist you?
It appears to be customary for monetary theorists to make use of equations in explaining their theories. Why do you think they have used this method? Do you think that such an equation is likely to clarify or becloud the theory to which it refers?

Source: Columbia University Archives. Albert Gailord Hart Papers, Box 60, Folder “Exams: Chi[ago] Qualifying”

Tags HartAG

Economists Exam Questions M.I.T. Suggested Reading Syllabus

MIT. Robert Solow’s Advanced Economic Theory Course, 1962

Post author By Irwin Collier
Post date 2016-09-22

Robert Solow taught the course Advanced Economic Theory at MIT in the Spring of the 1961/62 academic year. Of the dozen graduate students who took the course for credit were a future Nobel prize winner (Peter Diamond), a future Princeton professor and later member of Jimmy Carter’s Council of Economic Advisers (Stephen Goldfeld), a future professor at University of Pennsylvania/Washington University (Robert Pollak), a future professor and later chairman of Hebrew University (David Levhari), and a professor of economics and the first woman to head an MIT academic department, economics! 1984-1990 and MIT’s first female academic dean, School of Humanities and Social Science (Ann Friedlaender).

The three A’s awarded in the course went to Diamond, Levhari and Goldfeld.

The comprehensive exam questions for advanced economic theory from May 1962 were transcribed in the previous post.

_____________________________________

14.123—Advanced Economic Theory
Spring 1962—Professor Solow

FIRST READING LIST: LINEAR PROGRAMMING AND RELATED SUBJECTS

This should occupy 6-9 weeks. Most of the reading is in Gale: The Theory of Linear Economic Models and Dorfman, Samuelson, Solow: Linear Programming and Econmic Analysis, referred to below as G and D respectively.

Mathematical background: I hope to avoid spending any time on this. Mainly elements of matrix algebra—14.102 should be enough. For review, see D (Appendix B) and G (Ch. 2, more difficult).
Elements of Linear Programming; D (Ch. 2,3), G (Ch. 1,3).
Algebra and Geometry of Linear Programming, Simplex Method; D (Ch. 4, Sec. 1-11), G (Ch. 4).
Applications; D (Ch. 5-7), Manne: Economic Analysis for Business Decisions (Ch. 4,5).
Two-person zero-sum games; D (Ch. 15), G (Ch. 6,7).
Leontief and similar systems; G (Ch. 8, 9 Sec. 1-3), D (Ch. 9, 10).
Activity analysis; G (Ch. 9, Sec. 4), Koopmans: Three Essays on the State of Economic Science (pp. 66-104).
Von Neumann’s model; D (Ch. 13, Sec. 6), G (Ch. 9, Sec. 5-7).
Sraffa: Production of Commodities by Means of Commodities.
Robinson: “Prelude to a Critique of Economic Theory”, Oxford Economic Papers, February 1961, 53-58.
If time permits, the turnpike theorem; D (Ch. 12), Hicks: “Prices and the Turnpike”, Review of Economic Studies, February 1961, 77-88.
Radner: “Paths of Economic Growth that are Optimal, etc.”, Review of Economic Studies, February 1961, 98-104.

(Further references may follow.)

SECOND READING LIST: PUBLIC INVESTMENT CRITERIA

Hirshleifer: “On the Theory of Optimal Investment Decision”, Journal of Political Economy, August 1958, pp. 329-352.
Graaff: Theoretical Welfare Economics, Chs. 6-8.
Eckstein: “A Survey of the Theory of Public Expenditure Criteria”, in Public Finances: Needs, Sources and Utilization, with “Comments” by Hirshleifer.
Margolis: “The Economic Evaluation of Federal Water Resource Development”, AER, March 1959, pp. 96-111.
Steiner: “Choosing Among Alternative Public Investments”, AER, Dec. 1959, pp. 898-916.
Maass, al.: Design of Water-Resource Systems, Chs. 2, 13 (and passim).
Eckstein: Water Resource Development, Ch. 1-4.

_____________________________________

April 11, 1962

14.123—Exam

Answer all questions.

A function f of vectors x,y,… is called subadditive if f(x+y) ≤ f(x) + f(y) for all vectors x, y, and called superadditive if the inequality is reversed.
Consider the LP problem of maximizing C′x subject to Ax ≤ b. The value of the maximum is a function of C, b, and A. Show that it is a subadditive function of C and a superadditive function of b.
A firm can produce n commodities with a linear technology involving one activity for each commodity. Production involves only fixed factors, m in number, m<n, of which specified amounts are available. The output is sold at market prices p, and the firm chooses non-negative vector x of outputs to maximize p′x subject to the fixed-factor limitations.
(a) Prove that the supply curve is not negatively sloped; that is, prove that if p₁ increases, other prices constant, the optimal x₁ must increase or remain unchanged, but cannot decrease. (Hint: a straightforward procedure is to consider closely the final simplex tableau, the signs of various elements, and what can happen to require further iteration if p₁ There is a much simpler proof, comparing the before-and-after optima.)
(b) State and interpret the dual to the theorem just proved.
Consider a simple linear model of production, with 2 goods, and with 2 fixed factors, land and labor, available in specified amounts.
(a) Sketch possible shapes for the set of feasible net outputs, or net production-possibility curve.
(b) Suppose demand conditions are such that consumption expenditures on the two commodities are always equal. Give a complete analysis of the determination of the prices of the two goods and also the rent of land and the wage of labor. Graphical methods will help. (Hint: at one key point the construction of an isosceles triangle is very useful.)

Source: Duke University. Rosenstein Library. Robert M. Solow Papers, Box 67, Folder “14.123 Final Exam Fall-1969[sic|”.

Image Source: Robert Merton Solow at the M.I.T. Museum website.

Tags Diamond, Friedlaender, Goldfeld, Levhari, Pollak, Solow

Exam Questions M.I.T.

MIT. Advanced Economic Theory Exam, 1962

Post author By Irwin Collier
Post date 2016-09-22

Coming up will be the reading list(s) and exam for the course Economics 14.123 (Advanced Economic Theory) taught by Robert Solow in the Spring semester of the 1961-62 academic year at M.I.T.

_____________________

May, 1962

GENERAL EXAMINATION—ADVANCED THEORY

Answer question 1 and 3 others.

Make a catalog of the kinds of situations in which resource allocation through the price system is likely to give non-optimal results. Indicate the nature of the non-optimality, and for at least some of the situations describe the analytic reason why non-optimality results.

A consumer can buy n goods, x₁ … x_n, at prices p₁, … p_n. For each unit of x_i he purchases (for cash), he receives a_i trading stamps. He may then purchase further commodities for trading stamps at fixed trading-stamp prices w₁ … w_n.

Analyze his equilibrium in each of the following cases, interpreting your results in words and explaining how the equilibrium differs (if at all) from the no-trading-stamp equilibrium where all a_i = 0.

(a) a_i = k p_i; w_i = c p_i

(b) a_i = k p_i; w_i≠ c p_i

(d) a_i ≠ k p_i; w_i ≠ c p_i

Let A be a non-singular, indecomposable constant Leontief matrix. If this period’s outputs are immediately and exactly plowed back as inputs for next period and there is no capital or consumption:

(a) Set up the implied difference equation system.

(b) Is that system capable of balanced growth?

(d) Is the balanced growth ray unique?

(e) What optimality properties, if any, does balanced growth have?

(f) Is the balanced growth ray stable?

There are k countries, each with a fixed supply of a single scarce primary factor of production. In country i, it takes a_i units of the factor to produce a unit of wine and b_i units to product a unit of cloth.

(a) Formulate this k-country Ricardian comparative advantage setup as a linear programming problem for world efficiency, and show how the Ricardian results emerge.

(b) State and interpret the dual of the world-efficiency problem.

An investor has open to him all two-period investment options with net cash flows N₀ and N₁ such that N₀² + N₁² =1. He can lend unlimited amounts at an interest rate of 4 percent per period and borrow unlimited amounts at a rate of 6 percent per period. His preference for consumption in the two periods C₀ and C₁ are described by the utility function U = C₀ +(C₁)^½. Find the investor’s best plan of action.

A system uses primary labor and produced capital good(s) to produce consumption output and gross capital formation(s). Labor grows exponentially at the rate of g per annum. Suppose everything else matches that rate of growth. Show that consumption per capita is maximized where the interest rate, r, equals the growth rate, g. (Use any specific model, however simple or complex, to give your proof.)

Source: Duke University. Rubenstein Library. Edwin Burmeister Papers. Box 23.

Image Source: MIT beaver from the cover of the 1949 yearbook Technique.

Courses Exam Questions Suggested Reading

Harvard. European Central Banking. Schumpeter, 1945

Post author By Irwin Collier
Post date 2016-09-12

Course offerings in money and monetary policy at Harvard in the late 1930s and most of the 1940s were dominated by John H. Williams and Alvin Hansen. An exception was the course, “The Theory and Policy of Central Banking: European Experience,” that was offered just once (Fall term 1945-46) by Joseph Schumpeter. I was only able to find what appears to be a hastily assembled, provisional list of suggested readings provided at the start of the semester with a promise that “References to material and literature will be given currently”. The list of final examination questions for the course that I found in Schumpeter’s papers at the Harvard Archives at least gives us some indication of the broad themes of the course.

_________________________________

Course Enrollment

[Economics] 142a. (fall term) Professor Schumpeter.—The Theory and Policy of Central Banking: European Experience.

4 Graduates, 1 Junior, 5 Public Administration, 1 Radcliffe: Total 11

Source: Harvard University, Report of the President of Harvard College and Reports of Departments for 1945-46, p. 60.

_________________________________

HARVARD UNIVERSITY
1945-6
Economics 142a

This course aims at working out the role of central banks both in the capitalist and in the planned economy, and at reviewing a number of theoretical and historical problems in the field of money and credit, relevant tot he main theme. References to material and literature will be given currently. The following list is confined to general suggestions.

General works on central banking.

A. C. Conant, History of Modern Banks of Issue, 6^th ed., 1927.
C. H. Kisch and W. A. Elkins, Central Banks*, 1928.
E. Victor Morgan, Theory and Practice of Central Banking, 1797-1913, 1942.
V. C. Smith, The Rationale of Central Banking, 1936.
R. G. Hawtrey, The Art of Central Banking*, 1932.
M. H. de Kock, Central Banking, 1939.

Works on the History of Banking Theory.

W. T. C. King, History of the English Discount Market*, 1936.
H. E. Miller, Banking Theories in the U. S. before 1860, 1927.
E. Wood, English Theories of Central Banking Control, 1819-1858, 1939.

For Prewar Figures on Central Banks, see

League of Nations, Money and Banking 1938-9, Vol. I, 1939.

Miscellaneous Suggestions.

J. W. Angell, The Behavior of Money, 1936.
P. Einzig, The Theory of Forward Exchange, 1937.
C. R. Whittlesey, Bank Liquidity and the War, (National Bureau of Economic Research, Our Economy in War, Occasional Paper 22).
A. Youngman, The Federal Reserve System in wartime, (the same, Occasional paper 21).

* These are especially recommended.

Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003, Box 4, Folder “Economics, 1945-46 (2 of 2)”.

_________________________________

Final Examination Questions

1945-46

HARVARD UNIVERSITY
ECONOMICS 142A

One question may be omitted. Arrange your answers in the order of the questions.

Discuss the issue: “Control of Money” or “Control of Credit.”
If you were to frame the plan for a Central Bank, for instance in one of the South-American states, would you give it the right to do business with customers other than banks?
In 1910, the Governor of the Bank of England declared that the following types of finance bills were “legitimate”: (a) bills that represent exchange transactions; (b) bills created in order to finance the carrying of stocks of commodities or securities; (c) bills drawn in anticipation of public loans. Comment.
Suppose that a country which has been using paper money, adopts an unrestricted gold standard. Disregarding the period of transition, would you expect Bank Rate to keep on a higher level after the gold standard has been established than it did under the paper standard? Assume that the rest of the world is on the gold standard.
State the main points of difference between the constitutions and policies of the Bank of England, the Bank of France and the Bank of Germany in the last quarters of the 19^th century and explain briefly their significance and causes.
Explain the reasons for the decline in importance of the Domestic Bill during the half-century before 1914. Had this decline anything to do with the legislation about central banks? And had it, in turn, any influence upon their policy?

Final. January, 1946.

Source: Harvard University Archives. Joseph Schumpeter Papers. Lecture Notes, Box 3, Folder “misc. notes”.

Image Source: Selection from “Joseph A. Schumpeter and other at dinner table, ca. 1945”, Harvard University Archives HUGBS 276.90p (4).

Tags Schumpeter

May 22, 1959 General Examination in Macroeconomics

I.

II.

III.

February 8, 1960 GENERAL EXAMINATION IN ECONOMIC THEORY

PART I

PART II

Comprehensive Exam Grades in Macro Theory MIT Feb. 1960

September 19, 1960 General Examination in MACROECONOMICS

I.

II.

Macroeconomics Grades Sep. 1960

February 6, 1961 GENERAL EXAMINATION IN ECONOMIC THEORY Part II—Macroeconomics—Two Hours

Part I.

Part II.

May 22, 1961 GENERAL EXAMINATION IN ECONOMIC THEORY Macroeconomics—Two Hours

Part I.

Part II.

General Exam Grades “MacroTheory” May 22, 1961

September 18, 1961 GENERAL EXAMINATION IN ECONOMIC THEORY Macroeconomics—Two Hours

Part I.

Part II.

February 5, 1962 GENERAL EXAMINATION IN ECONOMIC THEORY Part II—Macroeconomics TWO HOURS

Part I.

Part II.

May, 1962 GENERAL EXAMINATION—MACROECONOMICS

PART I

PART II

September 17, 1962 GENERAL EXAMINATION IN ECONOMIC THEORY Part B—Macroeconomics

TWO HOURS

Part I

Part II

Part III

GENERAL EXAMINATION IN MACROECONOMICS February 4, 1963

Part I.

Part II.

Part III.

General Examination in Macroeconomics May 13, 1963

I.

II.

September 16, 1963 GENERAL EXAMINATION IN MACROECONOMICS TWO HOURS

Part I.

Part II.

General Examination Grades in Macroeconomics September 1963

February, 1964 GENERAL EXAMINATION IN ECONOMIC THEORY MACROECONOMICS—TWO HOURS [Note: this exam recycled in February, 1968]

Part I

Part II

February 8, 1965 GENERAL EXAMINATION IN MACROECONOMICS TWO HOURS

Part I.

Part II.

May 17, 1965 GENERAL EXAMINATION IN MACROECONOMICS TWO HOURS

Part I.

Part II

September 13, 1965 GENERAL EXAMINATION IN MACROECONOMICS Two Hours

PART I.

PART II.

February 7, 1966 GENERAL EXAMINATION IN MACROECONOMICS Two Hours

PART I:

PART II:

May 13, 1966 GENERAL EXAMINATION IN MACROECONOMICS Two Hours

PART I

PART II

February, 1968 GENERAL EXAMINATION IN ECONOMIC THEORY MACROECONOMICS—TWO HOURS [Note: recycled exam from February, 1964]

Part I

Part II

14.452 FINAL EXAMINATION May 23, 1968

Part I

Part II

Part III

GENERAL EXAMINATION IN ECONOMIC THEORY Macroeconomics—Two hours Sept. 1968

PART I

PART II.

Spring, 1969 GENERAL EXAMINATION IN MACROECONOMICS Three Hours

PART I

PART II

PART III

General Examination Grades in Macroeconomics Spring 1969

MACRO GENERAL February 3, 1971

A

B

May 22, 1959
General Examination in Macroeconomics

February 8, 1960
GENERAL EXAMINATION IN ECONOMIC THEORY

Comprehensive Exam Grades in Macro Theory
MIT Feb. 1960

September 19, 1960
General Examination in MACROECONOMICS

Macroeconomics Grades
Sep. 1960

February 6, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Part II—Macroeconomics—Two Hours

May 22, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two Hours

September 18, 1961
GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two Hours

February 5, 1962
GENERAL EXAMINATION IN ECONOMIC THEORY
Part II—Macroeconomics
TWO HOURS

May, 1962
GENERAL EXAMINATION—MACROECONOMICS

September 17, 1962
GENERAL EXAMINATION IN ECONOMIC THEORY
Part B—Macroeconomics

GENERAL EXAMINATION IN MACROECONOMICS
February 4, 1963

General Examination in Macroeconomics
May 13, 1963

September 16, 1963
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

February, 1964
GENERAL EXAMINATION IN ECONOMIC THEORY
MACROECONOMICS—TWO HOURS
[Note: this exam recycled in February, 1968]

February 8, 1965
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

May 17, 1965
GENERAL EXAMINATION IN MACROECONOMICS
TWO HOURS

September 13, 1965
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

February 7, 1966
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

May 13, 1966
GENERAL EXAMINATION IN MACROECONOMICS
Two Hours

February, 1968
GENERAL EXAMINATION IN ECONOMIC THEORY
MACROECONOMICS—TWO HOURS
[Note: recycled exam from February, 1964]

14.452
FINAL EXAMINATION
May 23, 1968

GENERAL EXAMINATION IN ECONOMIC THEORY
Macroeconomics—Two hours
Sept. 1968

Spring, 1969
GENERAL EXAMINATION IN MACROECONOMICS
Three Hours

General Examination Grades in Macroeconomics
Spring 1969

MACRO GENERAL
February 3, 1971

GENERAL EXAMINATION IN MACROECONOMICS
June 24, 1971
TWO HOURS

14.123—Microeconomic Theory III
Theory of the Consumer and Resource Allocation

Professor Hal R. Varian, E52-353, 3-2662
Spring, 1975

14.123 Spring, 1975
Professor Hal R. Varian

14.123 Spring, 1975
Professor Hal R. Varian

14.123 Spring, 1975
Professor Hal R. Varian

14.123 Spring, 1975
Professor Hal R. Varian

14.123 Spring, 1975
Professor Hal R. Varian

14.123 FINAL EXAMINATION
March 19, 1975

Waiver Exam—14.122
September 11, 1974

14.122
November 1, 1974

One hour and a half
Answer any FIVE of the following six questions:

READING LIST FOR 14.124
P. A. Samuelson
SPRING 1975

FINAL EXAM
14.124
MAY 20, 1975

Examination in Economics 301
Winter Quarter, 1935-

Paul Samuelson’s response to Jacob Viner, 1963
Carbon copy

Economics 115
Final Examination
January, 1951

UNIVERSITY OF TORONTO
FACULTY OF ARTS

ECONOMICS 3e, 3h
MONEY, CREDIT AND PRICES

14.123—Advanced Economic Theory
Spring 1962—Professor Solow

HARVARD UNIVERSITY
1945-6
Economics 142a

HARVARD UNIVERSITY
ECONOMICS 142A