Category: Exam Questions

My curating strategy generally has been to post individual artifacts one by one with each limited to a specific university, a particular point in time and a single course/field. But sometimes, just sometimes, I stumble upon a relatively complete, long-run of comparable artifacts to warrant lining them up into a single post. 

In William J. Baumol’s papers in the Economists’ Papers Archives at Duke University, we find about two decades’ worth of post-war Ph.D. general exams in economic theory at Princeton. 

But wait, there is more…

Scans of the microeconomic theory general exams for 1987-1989 and 1990-1994 at Princeton can be downloaded from the Ed Tower Collection at Duke.

____________________________

May 1953

PRINCETON UNIVERSITY
Department of Economics and Social Institutions

General Examination
for the Degree of Doctor of Philosophy
Theory

May, 1953

Part I

Answer any three

I

Discuss the problem of cost calculation and pricing in a multi-product firm, touching on problems like overhead costs and technical variability and invariability of output proportions.

II

Is there a theory of wages? Describe what has been done in the literature on the subject and indicate why the initial question might be raised at all.

III

“Monopoly tends to restrict output to undesirably small levels.” Discuss.

IV

How would you show by indifference curve analysis that out of larger incomes larger amounts will be saved. Is such a proposition empirically plausible.

Part II

Define any four

1. 1. Cross elasticity of demand
   2. Economic horizon
   3. Marginal efficiency of capital
   4. Average period of production
   5. Consumer’s surplus
   6. Linear programming.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

May 1955

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy
May 1955

Economic Theory

Answer any four. Try to be brief and to the point.

I

If a monopolist sells in two separated markets with similar costs but different demand curves, prove that it will be profitable to charge a lower price in the market where the elasticity of demand is greater.

II

Explain the relation between the rate of interest and the price of bonds and show how Keynes uses this in arguing that there is a floor to interest rates.

III

Construct a contract curve. Show that for any point on the contract curve a) the marginal rates of substitution between the two commodities will be equal for both parties,  b) no change can benefit one of the two parties without adversely affecting the other.

IV

Keynes argues that a fall in money wages will not reduce real wages because prices will fall proportionately. Explain how this could come about considering that labor costs are only a fraction of total costs and that workers provide only a fraction of the demand for goods.

V

Discuss the argument that a nationalized industry ought to sell its output at a price equal to its marginal cost.

VI

Discuss the policy implications of the monopolistic competition theory of the output and pricing by the firm.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

October 1955

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

ECONOMIC THEORY

Mr. George K. Chacko
October, 1955
(Time: three hours)

Answer any three

I

1. On what ground has it been argued that a nationalized industry should charge a price equal to its marginal costs?
2. Why has it sometimes been argued that this rule will produce undesirable results unless all industries are nationalized?
3. How would the presence of external economies or diseconomies affect this rule?

II

1. Define a contract curve.
2. Show its geometric construction.
3. Show that corresponding to any point off the contract curve there is a point on the curve which represents an improvement to both parties.
4. Show that no move from a point on the contract curve can possibly represent an improvement to both parties.

III

1. Define the acceleration principle.
2. Show that it implies a one quarter cycle lag in consumption behind investment.
3. How can this get the underconsumptionists out of an embarrassing position?

IV

1. Define price elasticity of demand.
2. Assuming nothing but the definition prove that a fall in price will raise a consumer’s expenditures on an item if his demand for it is elastic.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

January 1956

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

January, 1956

Economic Theory

Answer any four questions.

1. Outline a) Keynes’ interest analysis and
   b) one classical analysis of the determination of the rate of interest.
   c) Show how a neo-classicist might accept the Keynesian position for the short and yet argue consistently that in the long run the rate of interest will be determined by “real” relationships.
2. a) What is the marginal condition for the equilibrium of exchange of two commodities between two consumers?
   b) Show that if the conditions are not satisfied it is possible for these consumers to arrange for a mutually beneficial exchange.
   c) Show these results diagrammatically.
3. a) Show the circumstances under which price and quantity sold on a competitive market for the product of one industry will tend toward their supply demand equilibrium values.
   b) When will they not tend toward equilibrium?
   c) What is the significance of this point for practical application of the static equilibrium analysis?
4. a) What are external economies of scale?
   b) Show how they can prevent achievement of an ideal allocation of resources in a competitive free enterprise economy.
   c) Show how they might lead to a misallocation of resources by a competitive industry though they might have no analogous effect on a monopolistic firm which takes over that industry.
5. a) Describe the Neumann-Morgenstern index of utility.
   b) How does it differ from utility measurement in the classical sense?
   c) What is meant by measurement unique up to a linear transformation, i.e., what does the mathematician mean by cardinal measurement?
6. a) Define the income effect on the quantity of x of a change in the price of x.
   b) Show that in the case of the sale of a commodity out of a fixed total supply, the income effect on the amount offered by the supplier will usually be opposite in sign from the substitution effect.
   c) Show how this may be used to account for union demands for a shorter work week despite higher hourly wages.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

October 1956

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

October, 1956

Economic Theory

Time: 3 hours
Answer any three questions.

I

1. Show how in Keynesian theory an increase in money supply will have some effects in common with a fall in money wages.
2. What difference can be expected in their effects on expectations?
3. Why does Keynes argue for one against the other?
4. What is the Pigou effect?

II

1. In terms of indifference curves show the effects of a tariff on the terms of trade.
2. What is the relation to the contract curve?
3. Show why the point of competitive equilibrium in the absence of tariff is supposed to lie on the contract curve.

III

1. Describe the Neumann-Morgenstern utility index.
2. What is meant by its being cardinal?
3. Prove the relevant properties.

IV

Discuss the stability of equilibrium under Marshallian and Walrasian assumptions including such considerations as long run vs. short run and forward falling vs. backward rising supply curves.

V

Show why it is maintained that ideal output can be achieved when price is everywhere equal to marginal cost.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

January 1957

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

January, 1957

Economic Theory

Part I

Answer any three questions.

I

Show that the Laspeyres index of real income for an individual will always be correct when it shows his real income has fallen but may be wrong when it indicates his real income has risen.

II

Describe the identification problem and indicate what can be done about it. Use the Keynesian model rather than the supply-demand diagram as an illustration.

III

Describe the marginal and second order conditions of equilibrium for the output of two commodities produced by a single firm under pure competition (i.e. when will the relative outputs of the two items be optimal?) Show why these conditions are valid, and illustrate in a diagram.

IV

Describe the loanable funds and liquidity preference theories and some of the attempts to show that they amount to the same thing.

Part II

Answer any question.

I

What does Patinkin mean by the real balance effect? Why does he state that the price level will be indeterminate in its absence? Where does this leave the quantity theory?

II

What is ideal output? What price conditions are usually said to be enough to assure its achievement? Explain and criticize.

III

What is the point input-point output case in capital theory? Why is it particularly easy to define an average period of production in this case?

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

May 1957

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

May, 1957

Economic Theory

Time: 3 hours

PART I
(Answer all questions)

1. (a) Explain how for close substitutes the marginal utility of X might fall as the quantity of X in increased but that of Y is increased.
   (b) Give a concrete illustration.
   (c) Explain intuitively why the consumer in not in equilibrium if the marginal rate of substitution of A for B is not equal to the ratio of their prices.
2. (a) Explain why in the Keynesian system a fall in taxes will shift the savings curve to the right (Hint: Here the savings figure is based on income before)
   (b) Why does this result appear paradoxical?
   (c) Show diagrammatically that this shift in the savings curve will increase equilibrium national income.
3. (a) Show diagrammatically how prices are determined in its two markets by a discriminating monopolist.
   (b) Why must equilibrium marginal revenue be the same in both markets?
   (c) Will discriminating monopoly output tend to be higher or lower than under simple monopoly? Briefly indicate an intuitive reason for your answer.

PART II
(Answer one question)

1. Discuss the issues in the marginal cost controversy.
2. Describe the theory of marginal pairs.
3. Discuss the Scitovsky and Kaldor criteria.
4. Discuss the average period of production and its use in interest theory.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

October 1958

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

October, 1958

Economic Theory

Time: Three hours

I

Discuss the relationship of Say’s Law, Walras Law and the determinateness of the price level in a General Equilibrium system.

II

Describe and evaluate any two standard duopoly or bilateral monopoly models.

III

State and explain the basic assumption of the revealed preference analysis of consumer behavior. Derive at least one theorem with its aid and describe its implications for index number theory.

IV

What is the real balance (Pigou) effect? How does it enter the analysis of effects of a general wage cut on employment? Discuss the relevant interest rate mechanism.

V

What are external economies and diseconomies? How do they make possible competitive equilibrium in an industry in which the average cost curve is downward sloping? What are the implications of external economies for the relationship between competitive and “ideal” resource allocation?

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

October 1959

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

October, 1959

Economic Theory

Time: 3 hours

I. (answer four questions)

1. —

1. 1. What is the real balance (Pigou) effect?
   2. Explain its role in the determination of the price level.
   3. What is its role in the relation between wages and employment?

2. —

1. 1. Define the income effect.
   2. Show that the substitution effect involves a fall in the demand for a commodity when its price increases.
   3. Draw an indifference map which corresponds to a positively sloping demand curve.

3. Describe two oligopoly models in detail.

4. —

1. 1. Draw a curve of marginal fixed costs and explain its shape.
   2. What does this result imply about the effect of a change in fixed costs on the price and output of a profit maximizing firm? Explain.
   3. Does the same result necessarily hold for a firm with other objectives? Explain.
   4. Derive and criticize the theorem that perfect competition yields an ideal allocation of resources.

[note: file only has this first page of the October 1959 exam. Presumably there was at least a Part II and perhaps Part III/IV….?]

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1950-59)”.

____________________________

January 1960

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

January, 1960

Economic Theory

PART I
(Answer all Questions)

1. [Linear homogeneous production function]
   1. Define “Linear homogeneous production function.”
   2. Name two areas in economies in which such functions occur in the literature and indicate their role briefly.
2. Keynes at some point appears to assert that a fall in money wages does not reduce real wages.
   1. How may this be explained (in your answer take account of the fact that labor cost is only a part of total cost)?
   2. Does Keynes ever indicate that a fall in money wages might increase employment? If so, how would the process work?
3. Compare the analyses by Lange and Patinkin of the role of money in neo-classical systems.
4. Assume a purely competitive system with only one non-produced, scarce factor—labor. Also, assume the only capital in the economy is in the form of a single type of machine.
   1. in every industry using the machine it is “productive” in the sense that for given amounts of cooperating labor and intermediate goods, more is produced with it than without it. Is this necessary for interest to be paid to owners of the machines? Is it sufficient?
   2. if machines are only labor and are sold at long-run average coat, how can their owners get more from them than the recovery of these costs?
   3. “Wicksell was misleading in his explanation of interest, because he placed so much emphasis upon the productivity of the machine in the above example, while Böhm-Bawerk was misleading because he placed so much emphasis upon consumer psychology. Both elements are necessary to an explanation of the level of the interest rate.” Do you agree? Explain.

PART II
(Answer any two questions)

1. Discuss the welfare effects of monopoly from the point of view of resource allocation.
2. (a) Describe and discuss the “minimum critical effort” thesis in the theory of economic development. (b) What is the role of external economies in the literature of economic growth?
3. Compare and contrast the major theories of profits.
4. Discuss each of the following statements:
   1. “Marx was right in stressing that labor should receive its average. If all factors are given their average, rather than their marginal products, the product will be exhausted and we need not worry about whether the production function is or is not linear and homogeneous.”
   2. “It is fundamentally impossible to determine how much of a product has been produced by the labor contained in it, how much by the capital, and how much by the land. Any distribution theory must, therefore, be fortuitous in spite of any seeming scientific quality. It cannot be based on relative contributions by factors to the product.”
   3. “To instruct me to pay every laborer his marginal product is not to tell me how much labor to hire. Suppose I am a farmer. The first man I hire at $40/per week, his marginal product. The second man I hire for $38.20, his marginal product, and so forth. But the theory of marginal productivity tells me to go on hiring in this way indefinitely.”

WJB-REK: rhm

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1960

PRINCETON UNIVERSITY
Department of Economics and Sociology

General Examination
for the Degree of Doctor of Philosophy

May, 1960

Economic Theory

Answer all questions.

I.

“Keynes’s General Theory is merely a subcase of the neoclassical theory of employment. In the latter, if the money wage-rate is inflexible downward, unemployment can result. The introduction of the rigid money wage-rate by Keynes yields such rigidity and unemployment. If one removed the assumption that the supply of labor was a function of the money wage-rate, and assumed instead it was related to the real wage-rate, no underemployment equilibrium could exist in Keynes’s model.” Discuss.

II.

(a) Assume that capital goods are fixed in quantity, are indestructible, and non-producible. Assume, also, the existence of a stationary state. Further, abstract from all monetary phenomena,

1. 1. Under what conditions would capital goods receive returns? How would such returns differ from rents to natural resources?
   2. Would an interest rate exist in this economy? If so, would it be positive or negative?

(b) Assume, now, that capital goods are subject to wear and tear, must be replaced if the capital stock is not to decline, and are producible. The stationary state is again assumed, and monetary phenomena are abstracted from.

1. 1. Schumpeter believed the interest rate in such an economy would be zero. How could this occur?
   2. Capital goods are “productive.” If the interest rate were zero, so that their owners received no net returns, would this contradict the proposition that capital goods contribute a net product to the society?
   3. Wicksell believed the interest rate in this economy would be positive. But, since capital goods are merely land and labor in a different physical form, this would imply that amounts of land and labor in one form would be paid more than the same amounts in merely different physical form. Explain.

III.

Briefly:

1. 1. What is the level of current United States gross national product at an annual rate?
   2. What proportion of it goes for consumption, gross investment, and all-levels-of-government usage?
   3. What is the current rediscount rate at the Federal Reserve Banks?

IV.

“Let A, B, C, and D be four baskets of goods, and U_a, U_b, U_c, and U_d be von Neumann-Morgenstern ‘utility’ measures of an individual’s preferences among them. These utility measures are ordinal for choices under conditions of certainty, but cardinal for choices under conditions of risk.”
Do you agree or disagree? Explain.

V.

“For a firm with no effect on product or factor prices, maximization of profits requires that marginal physical products of all factors be proportionate to factor prices. Yet sometimes it is said that maximization of profits requires that marginal value products be equal to factor prices. These conditions are not equivalents and one or the other does not hold when profits are maximized.”
Explain.

VI.

Answer either (a) or (b).

(a) A firm sells two products, A and B, which it may produce jointly by two linear, infinitely divisible processes whose vectors are given below:

Process 1

Process 2

where inputs are treated as negative quantities, and:

(1) j^xa and j^xb are outputs of A and B from process j;

(2) j^xc and j^xb are inputs of labor and capital into process j;

(3) j^c1 and j^c2 are inputs of plant and warehouse capacity into process j.

The firm has given plant capacity of 200 units per period and warehouse capacity of 1000 units per period. Prices are given at

p_a = 4, p_b = 6, p_c = 3, p_d = 1.

What are the firm’s optimal process levels?

(b) A Leontief [1 – a] matrix is given below:

                  What levels of gross output are required to produce the following bill of goods:

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1961

PRINCETON UNIVERSITY

General Examination
for the Degree of Doctor of Philosophy

May, 1961

Economic Theory

1. (a) State and explain the basic premise of the revealed preference theory.
   (b) Explicitly use this premise to derive the sign of the substitution effect.
   (c) Under what circumstances would you expect the premise to be violated in practice?
2. (a) What is “Walras’ Law” and what is its rationale?
   (b) How is it related to Say’s law?
   (c) How is Walras’ law employed in the basic equilibrium model?
   (d) How is it employed in Patinkin’s central argument?
3. (a) Explain the basic multiplier formula.
   (b) Explain the multiplier geometric series.
   (c) Discuss the balanced budget multiplier theorem.
4. Why is marginal cost pricing sometimes recommended as a rule for nationalized industries and what are its limitations?
5. In not more than one paragraph for each give a (necessarily) superficial characterization of
   (a) Nassau Senior’s contribution to interest theory
   (b) Marshall’s “two blades of the scissors”
   (c) The wages fund doctrine
   (d) The German academic position on economics at the beginning of the twentieth century.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1962

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1962

Economic Theory

Time: 3 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you obtain in the Office of the Department of Economies.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

1. —
   1. Define Pareto optimality
   2. Given two commodities A and B and two consumers 1 and 2, prove that if both commodities are bought by both consumers the situation will not be Pareto optimal unless
      (1) MU_a1 / MU_b1 = MU_a2 / MU_b2
      where MU_a1 is the marginal utility of commodity A to consumer 1, etc.
   3. What happens to condition (1) if consumer 1 purchases same of B but none of A and consumer 2 purchases some quantity of each item? (Give the new condition and explain briefly.)
   4. Show that if the prices of A and B are arbitrarily fixed at any levels, P_a and F_b respectively, and if both consumers are rational and each buys both items that condition (1) will automatically be satisfied without any direct central intervention, planning or rationing.
   5. Indicate briefly what this means, and what it does not mean, about the desirability of a price system.
2. —
   1. Assuming that the demand for money is dependent on the rate of interest and on the level of real income, show diagrammatically how a change in the quantity of money will affect the levels of investment, consumption, income and employment.
   2. State the grounds on which it is sometimes argued that a change in the rate of interest is unlikely to have a significant effect on the level of investment.
   3. Describe the process by which, according to Keynes, a fall in wages may increase the level of employment.
   4. Describe an alternative mechanism whereby a wage reduction can have this effect.
   5. How do these mechanisms conflict with the identity-form of “Say’s law”?
3. Assume that men and women are equally efficient in a certain occupation but the conditions of supply of men and women workers are different; that it is possible for the employer to pay different wage rates to men and women; and that there are no trade unions. With the marginal net productivity curve and the two labor supply curves given, show in a graph the wage rates the employer will pay and the numbers of men and of women he will employ.
   (Exact geometric construction is essential.)
4. Reasoning along the lines of Böhm-Bawerkian capital theory, assume that land is abundant and that there are two, and only two, alternative ways of using labor in the production of consumers goods: one without any roundabout-ways and another with an average investment period of one year. With the latter method, labor is 20 per cent more productive than with the former.
   1. that the rate of interest will be 20 per cent;
   2. that the interest rate will be zero, and wages will be determined by the productivity of labor used in the more productive way;
   3. that the rate of interest might be anything between zero and 20 per cent;
   4. that the rate of interest might be well above 20 per cent.

Discuss each of these alleged possibilities and state any additional assumptions needed for it to be realized.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

October 1962

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

October, 1962

Economic Theory

3 hours

1. —
   1. Define the acceleration principle.
   2. Describe some alternative hypotheses about the determination of aggregate investment by decision makers.
   3. Prove that if fluctuations are perfectly regular and symmetrical, a constant accelerator coefficient will yield an investment cycle which anticipates fluctuations in investment output by precisely 1/4 of a cycle.
2. —
   1. Describe the determination of wages as a bilateral monopoly process.
   2. Describe the role of linear homogeneous production functions in the theory of distribution.
   3. Discuss briefly why it has been considered appropriate to develop a theory of capital which is distinct from the general theory of distribution.
3. —
   1. Argue by numerical example that if for two commodities, x and y,  MU_x/P_x > MU_y/P_y it will normally pay the consumer to purchase more of x. here P_x is the price of x, MU_x, is the marginal utility of x, etc.
   2. Show the same result diagrammatically.
   3. Under what circumstances does MU_x/P_x > MU_y/P_y become an equilibrium condition?
4. —
   1. Write out a two constraint three variable cost minimization linear programming problem.
   2. Give an economic interpretation of the constraints and all the variables (including slack variables).
   3. Write out the dual of your problem.
   4. Interpret all of its variables economically.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1963

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1963

Economic Theory

Time: 3 hours

1. —
   1. Define the “Real Balance Effect”.
   2. Explain the grounds on which Patinkin maintains that it is necessary for consistency of a classical monetary system.
   3. Describe its role in the mechanism which equilibrates the price level.
   4. Evaluate the significance of the real-balance effect in the real world. What are some of the other mechanisms which may help to stabilize the price level in practice?
2. —
   1. Outline the Lutz-Hicks analysis of the structure of interest rates.
   2. How does this analysis account for the fact that long rates are frequently higher than short rates?
   3. What does this analysis assume about expectations?
   4. On what grounds can the analysis be criticized?
3. —
   1. Explain in terms of an indifference map how one might obtain a backward-rising supply curve of labor. (You need not draw the indifference map if you do not want to).
   2. Why in the case of the supply of a commodity are the income and substitution effects more likely to work in opposite directions, than in the case of demand?
   3. Do you believe that the supply curve of labor is typically backward sloping in practice? What evidence can you muster?
4. — Consider the following simplex matrix arising out of a problem of product line selection under profit maximization.

1. 1. Go through one pivoting step to find the next simplex matrix.
   2. Give the primal and dual solutions corresponding to your calculated matrix.
   3. Give an economic interpretation of each of the variable values in these solutions.
   4. State two of the duality theorems and show that they are satisfied by these solutions.

5. — Write one paragraph about each of the following:
   1. Von Thunen
   2. Nassau Senior
   3. Friedrich Bastiat.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

Undated, 1964-66[?]

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

Economic Theory

1. —
   1. Demonstrate geometrically the basic characteristics of the contract curve in the box diagram representing exchange between two parties.
   2. Show that the offer curves of the two parties will intersect at some point on the contract curve.
   3. What is the welfare significance of result (b)?
2. —
   1. Define: local maximum, global maximum, corner maximum, 2^nd order maximum conditions.
   2. In which of the three preceding types of maximum will the marginal (first order) equilibrium conditions normally break down (and why)?
   3. What is the relevance of the second order conditions for local and global maxima?
   4. In intuitive terms, what is the relationship, if any, between second order conditions and stability of equilibrium?
3. — “If the high price of corn were the effect, and not the cause of rent, price would be proportionately influenced as rents were high or low, and rent would be a component part of price. But that corn which is produced by the greatest quantity of labor is the regulator of the price of corn; and rent does not and cannot enter in the least degree as a component part of its price.”
   1. Who might have written this?
   2. Does this statement imply that the author supported either the theory of “differential rent” or of “scarcity rent?” Give reasons.
   3. What qualifications, if any, of the statement will be appropriate if corn production is only one of several possible uses of land?
4. —
   1. Discuss briefly the manner in which Say’s Law decomposes a general equilibrium model into real and monetary sectors.
   2. Relate briefly the Patinkin criticism of the neoclassical Invalid Dichotomy to your answer in 4 a.
   3. Relate briefly Walras’ Law to your answers in 4 a. and 4 b.
5. —
   1. What is the acceleration principle?
   2. Derive the multiplier formula.
   3. Discuss the multiplier effects of a balanced budget.
   4. Show how the accelerator can lead to a lagged relationship between investment and consumption.
6. — In not more than two sentences each characterize some of the work of the following:
   1. Jevons
   2. Bastiat
   3. Henry George
   4. Quesnay.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1967

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1967

Economic Theory

Time: 3 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you will have obtained from Mrs. Kwok.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

Part I.

Answer two questions. (15 points each)

1. Why is the measured government surplus not a good indicator of government fiscal policy actions to stimulate the economy? Does the size of the government surplus that would be realized at full employment serve to indicate unambiguously the amount of fiscal policy stimulus? Discuss the reasons for your answers.
2. One theory of investment emphasizes the importance of changes in output through the accelerator. Can this be incorporated within the view of investment as determined by the intersection of the marginal efficiency schedule and the marginal cost of funds schedule? Explain both theories in your answer.
3. In what sense do “vintage” capital models suggest that it is easier to change the capital intensity of the economy than did earlier models? How is labor allocated over different vintages if there is substitutability ex post as well as ex ante? Only ex ante substitutability?

Part II.

1. Discuss the following syllogism. (15 points)

Assumption. All markets are purely competitive.

Definition 1. Surpluses to factors are payments above the opportunity costs of those factors.

Definition 2. Profits are surpluses paid to entrepreneurs.

Major premise: in the long-run surpluses to factors do not tend to disappear.

Minor premise: profits are a type of surplus.

Conclusion: in the long-run profits do not tend to disappear.

2. Answer two of the following questions. (12½ points each)
   1. How does the Hicksian static analysis of the stability of equilibrium in multiple market economies differ from a dynamic stability analysis of such an equilibrium?
   2. Describe the structure and use of a Leontief static open input-output model.
   3. Does the income effect of a price change affect the behavior of a consumer in exactly the same way that it affects the behavior of a firm? Explain.

Part III.

Answer both 1. and 2. (15 points each)

1. —
   1. Explain with the aid of a numerical example why it would pay Sam Pfapfnfnik to readjust his allocation of money between bread and ink if the ratio of their two prices were unequal to the ratio of their marginal utilities to him.
   2. The price of ink falls but Sam does not change his ink purchases. Explain what is happening in terms of Sam’s indifference map between ink and other commodities.
   3. Assume that all of the increase in Sam’s purchasing power resulting from the fall in the price of ink is taxed away and that he consequently does not change his purchase of any commodity. The following would then appear to hold; the marginal utility of no commodity would have changed;
      P_i, the price of ink has fallen, so that if in the initial equilibrium—
      P_x/P_i = MU_x/MU_i then in the equilibrium position after the price fall it must be true that P_x/P_i does not equal MU_x/MU_i . How do you reconcile this result with your answer to part (a) of this question?

2. In one sentence for each, indicate something about the contribution of each of the following individuals:
   1. H. Gossen
   2. H. von Thunen
   3. Cairnes
   4. James Mill
   5. J. B. Clark
   6. E. Barone

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

October 1967

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

October, 1967

Economic Theory

Time: 3 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you will have obtained from Mrs. Kwok.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

Part I.

Answer two questions.

1. Define:
   1. income effect
   2. corner maximum
   3. homogeneity of degree zero
   4. Cobb-Douglas function
   5. revealed preference (a is revealed preferred to b)
   6. integrability (of an indifference map)
2. —
   1. Show precisely how, in a perfect capital market, the rate of interest enters the formula for the discounted present value of a stream of payments.
   2. Explain precisely why the rate of interest enters the formula in this way.
   3. If the capital market is imperfect so that the interest rate rises with the amount obtained by a borrower, how is your previous discussion affected?
3. —
   1. The cost and demand curves are linear and the same in two industries, one operated by a monopoly and one under pure competition. Precisely how will the magnitudes of the two outputs compare? Prove your answer.
   2. Explain how external economies make possible a decreasing long-run supply curve for a competitive industry.

Part II.

Answer any two questions.

1. What, in meant by the expressions “shocking” or “displacing the equilibrium of” a model and what can be learned by such procedures? Illustrate your answer with the standard income-substitution effect analysis of consumer theory. Discuss also the limitations of the techniques we now have for performing these displacements.
2. The following is an input-output model of the form
   [I – a][X] = [Y] for a two-sector economy:

.

Suppose [Y] = [10,20]. Solve the system for [X] and interpret your answers in economic terms.
Solve the system when [I – a] is as given below:

,

And interpret in economic terms.

3. Discuss the various concepts of “stability” in general economic systems analysis, including in your discussion the following comparisons:
   1. equilibrium vs. system stability
   2. global vs. local stability
   3. Hicksian vs. dynamic stability.

Part III.

Answer question No. 3 and either 1 or 2.

1. Give possible reasons for the existence of money illusion in each of the following Keynesian functions: consumption, labor supply, demand for money. How does the presence or absence of each of these effects alter the response of the Keynesian model to an open market purchase of bonds by the Central Bank?
2. For a non-monetary economy, what is the level of the interest rate in the classical stationary state, and why? Define carefully an analogous state for a growing economy. What factors determine the level of the interest rate? What is the “Golden Rule”, and what is its significance (if any)?
3. Assume that the President’s proposed 10% tax surcharge would raise personal and corporate tax liabilities by $3 billion each in fiscal 1968. Using multipliers that you think are reasonable, estimate the impact of this action on GNP and describe in words the way in which this impact will work itself out. You may assume that the Federal Reserve System’s goal is to keep the rate of inflation below 3% and that in the absence of monetary or fiscal restraint money GNP would grow at an annual rate of 8% (the CEA forecast).

Part IV.

In one sentence each characterize the writings of three of the following:

1. E. Barone
2. H. H. Gossen
3. F. Bastiat
4. Henry George
5. J. B. Clark.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1968

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1968

Economic Theory

Time: 3 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you have obtained from Mrs. Kwok.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

Part I. (25%)
Answer any two questions.

1. Present the essential points of the theories of income distribution expounded by
   1. Karl Marx,
   2. John Bates Clark (or another neo-classical writer),
   3. Michael Kalecki, and
   4. Nicholas Kaldor.
2. It has been said that the marginal-productivity theory of income distribution rests largely on technological facts (or assumptions), whereas aggregative theories of income distribution of the Kaldorian type rest chiefly on psychological facts (or assumptions). Attempt first to defend and then to criticize these contentions.
3. If the physical efficiency of labor increases in some industries but not in others, how would you expect the marginal productivities of labor in the various industries to change, assuming perfect mobility of labor and pure and perfect competition in all markets? After you have answered this question and explained your answer, proceed to point to the qualifications required (a) if mobility is restricted, (b) if some wage rates are fixed on the basis of collective bargaining with strong labor unions, and (c) if some industries enjoy a high degree of monopoly.
4. “Rent, like all prices, is a test, even though an imperfect one, of social need: its payment roughly ensures the most economical distribution of land between different uses; and its remission, by a land-owning State, to those in a position to pay it, whether private persons or public enterprises, would in general promote waste.” Explain every part of this statement.

PART II. (25%)
Answer question 1 and either 2 or 3.

1. Analyze the combined net impact of the two following actions:

1. 1. In a period of full employment with rising prices, the government raises transfer payments to the poor, financing the resulting deficit by selling Treasury bills to the Federal Reserve System. The Fed keeps the discount rate above the bill rate.
   2. The government also cuts spending on space programs by the same amount as it raises transfer payments, using the resulting savings to retire debt held by little old ladies who put the money in savings accounts.
2. While economists differ on the proportion of economic growth to attribute to investment in tangible capital, education, and research into new techniques, many would agree that these factors may be complementary with each other or complementary through time. Discuss the possible complementarities that may occur, identifying clearly the relationships and the effects such complementarities may have on the evaluation of investment policies.
3. Consider an economy in a classical stationary state with a positive interest rate determined by the interaction of productivity and time preference. If the discovery of the key to immortality wipes out time preference, while at the same time generating positive population growth, describe the resulting time path of the economy to a new “golden age” equilibrium.

PART III. (25%)
Answer two of the following questions.

1. Assume an economy with fixed amounts of two inputs, both of which are used in the production of each of two final goods.
   1. A necessary condition for efficient production is that the ratios of the marginal products of the inputs in the production of both goods be equal. Explain in economic terms why this must be true.
   2. Show how the production possibility frontier — the whole set of efficient output mixes — can be derived from the condition in (a) above.
2. Discuss each of the following statements. They are meant to be discussed separately.
   1. “In a purely competitive market economy a stationary state can exist only if the interest rate is zero, for every investment opportunity must be exhausted to have stationarity.”
   2. “Land in an economy with a zero interest rate must (a) have an infinite value and (b) earn a zero rate of return. These are contradictory, and so the interest rate can never be zero in a market economy.”
   3. “Marx was right. Labor sells its services for their discounted marginal product in an economy with positive interest rate. This is less than it creates, and therefore labor is exploited.”
3. Discuss the meaning and significance of the following concepts in general equilibrium theory:
   1. the law of conjugate pairs,
   2. the theory of second-best,
   3. the stability of a general economic system,
   4. balanced-growth equilibrium in a general system.

PART IV. (25%)
Answer question 1 and one of questions 2, 3, or 4.

1. —

1. 1. If demand is inelastic marginal revenue is ____________.
   2. If demand for a firm’s product is inelastic, a rise in its price
      1. will always increase profits.
      2. will always increase revenues but may not increase profits.
      3. we cannot tell from the information given.
   3. The price elasticity of a linear supply curve through the origin
      1. is unity.
      2. depends on the slope of the curve.
      3. will be higher the more firms in the industry.
      4. will be lower in the short-run.
      5. none of the above.
   4. Draw the indifference map for an item such as matches with perfectly inelastic demand for any price reduction.
2. —
   1. Make up a small linear programming problem.
   2. Write out its dual.
   3. Discuss in detail the economic interpretation of the dual.
   4. How might the values of the dual variables be used in economic planning?
3. The imposition of any arbitrarily chosen prices will mean that as far as exchange between any two consumers is concerned the Pareto optimality condition must be satisfied. Explain, proving any theorem you need for the purpose.
4. State three theorems on linear homogeneous production functions and prove one of them.

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1969

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1969

Microeconomic Theory

Time: 2 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you have obtained from Mrs. Kwok.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

Instructions: The examination consists of two parts which will be given equal weight. Spend about one hour on each part.

PART I.

1. Define:
   1. identification
   2. saddle point
   3. gross and net complements
   4. law of diminishing returns
   5. substitution effect
   6. Walras’ law
   7. lexicographical ordering.
2. Equilibrium of the firm under Chamberlinian monopolistic competition requires tangency between the firm’s average cost and demand curves. What do we know about the firm’s marginal cost and marginal revenue at that output? Prove your answer.
3. Describe one of the following:
   1. Kaldor’s model of distribution
   2. Arrow’s possibility theorem
   3. Fisher’s analysis of allocation of resources between present and future.
4. (Peak and off-peak pricing) An electric company plans for its output level x₁,…x₂₄ during each of the 24 hours of the day. Its operations are limited by its hourly generating capacity y so that its decisions are subject to the constraints

x_i < y  (i = 1, … , 24)

The firm’s prices are required by regulation not to vary with output

It seeks to maximize its profits, knowing its total operating cost function

C = f(x₁, … , x₂₄),

and the total cost of expanding its capacity

K = g(y)

1. 1. Prove that in any period in which the firm is not operating at capacity (an off-peak period) its profit maximizing price will be equal to its marginal operating cost. (Assume all outputs are positive: x_i > 0.)
   2. Prove that for peak periods the payments over and above marginal operating costs will sum up to the marginal cost of increased capacity.
2. In one sentence each characterize some of the work of the following economists:
   1. Henry George
   2. Thorstein Veblen
   3. H. H. Gossen
   4. F. Bastiat
   5. K. Wicksell.

PART II.

6. Give an example of an economic situation which does not satisfy the following hypotheses (using a separate example for each hypothesis):
   1. The consumption set for the ith consumer is convex.
   2. The preference relation of the ith consumer is strongly convex.
   3. The demand correspondence is upper semi-continuous.
7. Explain concisely why stability is a desirable property of general equilibrium models.
8. Consider a pure trade economy involving two individuals, Mr. A and Mr. B, and two commodities, 1 and 2. Assume that their initial holdings are

respectively, where

Suppose their indifference curves are specified by the utility functions:

1. 1. Show all Pareto-optimal states of the economy on an Edgeworth-box diagram.  Explain your answer.
   2. Find all initial holdings, for which

constitute a competitive equilibrium at some nonnegative prices (p₁, p₂). Graph your answer on an Edgeworth-box diagram.

9. Explain in concise terms the role of fixed point theorems in the theory of general economic equilibria.
10. What are the three main sources of comparative statics theorems?
    (EXTRA CREDIT: Give one example of each type of theorem.)

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Economics 506: History of Thought…1968-1990” [note: filed in incorrect folder].

____________________________

October 1969

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

October, 1969

Microeconomic Theory

Time: 2 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you have obtained from Mrs. Kwok.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Letter appears on each sheet or book.

PART I.

Answer THREE questions ONLY (20 ea)

1. Explain (5 ea)
   1. the relationship, between cost and the supply curve of the competitive firm.
   2. the relationship between cost and the supply curve of the competitive industry.
   3. What is the role of rent in the preceding relationship?
   4. How can the competitive industry be in equilibrium if its long run average cost curve is falling?
2. Describe one of the following:
   1. the Cournot duopoly model;
   2. the solution to a zero sum two person game;
   3. the notions of producers’ and consumers’ surplus and their graphic representation.
3. Construct a simple general equilibrium model discussing (7 ea)
   1. the significance of the number of equations as compared to the number of unknowns;
   2. the role of inequalities;
   3. the definition of existence end uniqueness and their significance.
4. —
   1. Define and discuss the significance of stability for general equilibrium models.
   2. State two non-trivial theorems about such stability.
5. Describe the Neumann-Morgenstern utility measure and its purpose.

PART II. (15 ea)

Answer every question.

1. —
   1. The elasticity of a straight line supply curve through the origin is __________.
   2. Prove the preceding answer.
2. —
   1. Give the formula for a Cobb-Douglas function.
   2. List two of its properties.
   3. Prove one of the two properties listed in (b).
3. Derive one of the following:
   1. The Slutsky theorem for a firm under perfect competition;
   2. The necessary conditions for optimal distribution of two commodities between two individuals..
4. —
   1. Nassau Senior
   2. F. H. Knight.
   3. John Bates Clark
   4. J. Dupuit
   5. Karl (sic) Menger

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1960-69)”.

____________________________

May 1970

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

May, 1970

Microeconomic Theory

Time: 2 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you have obtained from Mrs. Kwok.

Put PART I in one book and PART II in another. Be sure that your Code Letter appears on each sheet or book.

PART I. (50%)

1. Answer one question.
   1. Describe briefly one real and one monetary interest theory. Show how they can be reconciled.
   2. Explain the analysis leading to the conclusion that pure competition tends to yield an optimal allocation of resources.
   3. Describe the nature of the optimal solution to a zero sum two-person game including the notion of optimal mixed strategy.
2. Answer one question.
   1. A firm’s demand and average cost functions are linear with the general slopes usually assumed for them. Prove that the profit maximizing output will be half as large as the zero profit output, q₀ , where q₀ > 0.
      What are the second-order conditions here and what is their relevance?
   2. Prove that the feasible region for a linear programming problem is convex.
3. Answer both questions.
   1. Explain briefly the grounds on which the area under a demand curve above the level representing the market price is said to represent consumers’ surplus.
   2. In one sentence each, characterize some of the best known work of each of the following:
      1. the physiocrats
      2. The Austrian school
      3. Henry Wicksteed
      4. Wesley Mitchell
      5. James Mill

PART II. (50%)

Please answer four questions out of the following. Try not to spend any more than fifteen minutes on each question. Show all of your work. If you attempt more than four questions, then the best four will count.

1. The following assumptions are usually made in formulating a general equilibrium model. Give concise definitions of each and discuss their plausibility:
   1. nonincreasing returns-to-scale;
   2. no interdependence of decisions among economic agents;
   3. divisibility of goods and services.
2. What relationships can you identify between (linear and nonlinear) programming and the existence proofs for general equilibrium?
3. Illustrate graphically a case in which the competitive mechanism is not Pareto satisfactory. Describe in words how this case might occur in the real world.
4. State two general cases of economies in which global stability is always valid.
5. Distinguish between gross substitution and pure substitution. State a theorem in comparative statics that is a consequence of gross substitution.
6. Discuss the value of the models of general equilibrium theory for an economist who does not believe in the capitalist system. Comment on the criticism that such models merely “justify capitalism.”

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Exams (1970-79)”.

____________________________

October 1972

PRINCETON UNIVERSITY
Department of Economics

General Examination
for the Degree of Doctor of Philosophy

October, 1972

Microeconomic Theory

Time: 3 hours

Do not write your name on any of your examination papers, but identify them with a Code Letter which you have obtained from Mrs. Coleman.

Start a new paper or book for each question so that the examinations can be assembled by question rather than by candidate. Be sure that your Code Number appears on each sheet or book.

Answer three questions in Part I and three in Part II.

PART I.

1. —
   1. Given a nonlinear demand curve illustrate graphically how the corresponding marginal revenue curve can be constructed (no verbal explanation necessary).
   2. Give a rigorous proof of the validity of your construction procedure in a).
2. —
   1. Define the substitution effect on x of a change in the price of x.
   2. Prove the Slutsky Theorem about the sign of the substitution effect.
3. Given linear demand curves in two markets for a firm’s product, and a linear marginal cost curve for its output, show geometrically the prices and outputs in the two markets if the firm maximizes its profits and
   1. if it cannot discriminate in price between the two markets; and
   2. if it does discriminate.
4. —
   1. Explain the concept of Pareto optimality.
   2. In an Edgeworth box diagram show the locus of Pareto optimal points.
   3. What can be said about the desirability of a randomly chosen point off the locus relative to that of a randomly chosen point on the locus?
5. —
   1. Prove that if demand is inelastic a fall in price will reduce total expenditure.
   2. Describe the identification problem and show its implications for the empirical determination of a demand relationship.

PART II

6. —
   1. What is Say’s Law?
   2. What is homogeneity of degree zero in prices?
   3. Explain briefly how the two preceding assumptions cause difficulties for monetary theory.
7. —
   1. What is the issue of existence and uniqueness in a general equilibrium system?
   2. What is the relevance for this issue of the number of equations and the number of unknowns in the system? Illustrate your conclusion with concrete examples of equations, specifying their coefficients.
8. —
   1. Describe the Ricardian rent model, distinguishing between the extensive and the intensive margin.
   2. Show from this analysis why a tax on pure differential rent is not shiftable.
9. —
   1. What is the basic theorem of linear programming?
   2. Show diagrammatically why it does not hold in nonlinear programming.
   3. Explain in economic terms how the theorem is affected by the presence of diminishing returns.
10. —
    1. Define the acceleration principle.
    2. Draw a graph that assumes total output over the course of a cycle and has the form of a sine curve. Show then how investment must vary over time if it is determined by the acceleration principle.
    3. Show how your graph can mislead the unwary observer about the reasons for a downturn.

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library, Economist Papers’ Archive. William J. Baumol Papers, Box 20, Folder “Economics 506: History of Thought…1968-1990” [note: filed in incorrect folder].

Image Source: John E. Sheridan, Princeton Poster, c. 1901 . Library of Congress Prints and Photographs Division Washington, D.C. 20540 USA.