Category: Problem Sets

According to the class roll kept by Milton Friedman, we know that Gary Becker attended his graduate price theory course Economics 300A in the Autumn quarter of 1951 (presumably Becker then took 300B during the Winter quarter of 1952, but I could not find that quarter’s roll in Friedman’s papers). This post even has Friedman’s partial answer key for the True/False/Uncertain questions for Economics 300B!

The reading assignments for the two-quarter core price theory sequence taught by Milton Friedman in 1948 , and in 1958 have been posted earlier (1946 300A only).  This post gives the reading assignments with open and gated links where available (some of the papers are only available at the gated jstor.org). These can be compared to the readings for the price theory course Friedman taught at Columbia in 1939-40. 

I have put in boldface the 1951 additions to make a comparison with the 1948 version easier. Worth noting: an asterisk designates optional and not required reading.

Only one item was dropped from the 1948 reading list:

Meyers, A. L. Elements of Modern Economics, ch 5, 7, 8, 9.

The October 1951 version of the Reading Assignments for Economics 300A and B was published as an appendix to J. Daniel Hammond’s “The development of post-war Chicago price theory” in The Elgar Companion to Chicago School Economics, edited by Ross  B. Emmett, pp. 7-24. This Hammond article offers much context and is very much worth consulting.

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October, 1951

Economics 300A and B
Reading Assignments by M. Friedman

(Notes:

1. It is assumed students are familiar with material equivalent to that contained in George Stigler,  The Theory of Price. [Revised edition, 1952] or Kenneth Boulding, Economic Analysis [Third edition, 1955].
2. Readings marked with asterisk (*) are recommended, not required.)

Knight, F. H., The Economic Organization, esp. pp. 1-37. HB172.K73.
Keynes, J. N., The Scope and Method of Political Economy, ch. I and II, pp. 1-83. HB171.K45.
Hayek, F. A., “The Use of Knowledge in Society,” American Economic Review, Sept., 1945; Reprinted in Individualism and Economic Order. HB1.A6.

Marshall, Alfred, Principles of Economics, Bk III, ch 2, 3, 4; Bk V, ch 1,2. HB171.M36.
Friedman, Milton, “The Marshallian Demand Curve,” Journal of Political Economy, December 1949. YF6.
Schultz, Henry, The Meaning of Statistical Demand Curves, pp. 1-10. HB201.S398.
Working, E. J. “What do Statistical ‘Demand Curves’ Show?” Quarterly Journal of Economics, XLI (1927), pp. 212-27. HB1.Q3.
Knight, F. H. Risk, Uncertainty, and Profit, ch 3. HB601.K7. 1940.
*Lange, O., “On the Determinateness of the Utility Function”, Review of Economic Studies, Vol I (1933-34), pp. 218 ff. HB1.R45.
*Allen, R.G.D., “The Nature of Indifference Curves,” Ibid, pp 110 ff. HB1.R45.
Hicks, J. R., Value and Capital, Part I (pp 11-52). HB171.H64.
*Wallis, W. A., and Friedman, Milton, “The Empirical Derivation of Indifference Functions”, in Lange et al, Studies in Mathematical Economics and Econometrics. HB99.C5.
*Friedman, Milton and Savage, L. J., “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy LVI (August 1948) pp. 279-304. HB1.J7.

Marshall, Book V, ch 3, 4, 5, 12, Appendix H. HB171.M36.
Robinson, Joan, Economics of Imperfect Competition, ch 2. HB201.R65.
Clark, J. M., The Economics of Overhead Costs, ch 9. HB195.C62.
Viner, Jacob, “Cost Curves and Supply Curves”, Zeitschrift fuer Nationaloekonomie, Bd III (Sept, 1931), pp 23-46. H5.Z55.
Friedman, Milton, “The Relationships Between Supply Curves and Cost Curves,” (dittoed) YF9.
Chamberlin, Edward, The Theory of Monopolistic Competition, ch 3, sec. 1, 4, 5, 6; ch 5. HB201.C44.
Harrod, R. F. “Doctrines of Imperfect Competition”, Quarterly Journal of Economics, May 1934, sec. 1, pp. 442-61. HB1.Q3.
Stigler, G. J., “Monopolistic Competition in Retrospect,” Lecture 2 in Five Lectures on Economic Problems. HB171.S82.
*Triffin, Robert, Monopolistic Competition and General Equilibrium Theory, esp. Part II. HD41.T8 and H31.H33, v. 67.
*Robinson, E. A. G., The Structure of Competitive Industry. H045.R732.
*___________________, Monopoly. H041.R65.
*Plant, Arnold, “The Economic Theory Concerning Patents for Inventions,” Economica, Feb, 1934. HB1.E42.
*Dennison, S. R., “The Problem of Bigness,” Cambridge Journal, Nov. 1947. Y03.

Marshall, Book IV, ch 1, 2, 3; Bk V, ch 6. HB171.M36.
Clark, J. B., The Distribution of Wealth, Preface, ch 1, 7, 8, 11, 12, 13, 23.
Mill, John Stuart, Principles of Political Economy, Book II, ch 14. HB171.M667.
Hicks, J. R., The Theory of Wages, ch 1-6. HD4909.H63.
Smith, Adam, The Wealth of Nations, Bk I, ch 10. HB161.S652.
Marshall, Bk VI, ch 1-5. HB171.M36.
Friedman, Milton, and Kuznets, Simon, Income from Independent Professional Practice, Preface, pp. v to x; ch 3, Sec 3, pp. 81-95, ch 4, Sect 2, pp. 118-137, App, Sec 1 & 3, pp. 142-151, 155-61. HD4965.U5F8.
Knight, F. H. “Interest” in Encyclopaedia of the Social Sciences, also in Ethics of Competition. H04965.U5F8.
Keynes, J. M. The General Theory of Employment, Interest, and Money, ch 11-14. HB171.K46.
Weston, J.F., “A Generalized Uncertainty Theory of Profit,” American Economic Review, March, 1950, pp. 40-60. HB.A6.

Cassell, Gustav, Fundamental Thoughts in Economics, ch. 1, 2,3. Ch. 1, 2, 3. HB 179.C283.
_________________, The Theory of Social Economy, ch 4. HB179.C283.
J. R. Hicks, “Mr. Keynes and the ‘Classics’; A Suggested Interpretation”, Econometrica, vol 5, April 1937, pp. 147-159. HB1.E23, v. 5.
Franco Modigliani, “Liquidity Preference and the Theory of Interest and Money,” Econometrica, vol 12, No. 1 (Jan 1944) esp. Part I, sec. 1 through 9, sec 11 through 17, Part II, sec 21. HB1.E23, v.12.
A. C. Pigou, “The Classical Stationary State,” Economic Journal, vol 53, December, 1943, pp. 343-51. HB1.E3, v. 53.
____________, “Economic Progress in a Stable Environment,” Economica, 1947, pp. 180-90.HB1.E42, v. 14.
Patinkin, Don, “Price Flexibility and Full Employment,” American Economic Review, XXXVIII, 4, Sept. 1948, pp. 543-64. YP6.

Source: Hoover Institution Archive, Milton Friedman Papers, Box 77, Folder 1 “University of Chicago, Economics 300 A & B”.

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Economics 300A
Autumn, 1951
PROBLEMS FOR READING PERIOD

1. In an anti-trust case against the Aluminum Company of America, Judge Learned Hand argued that the Aluminum Company could be regarded as having essentially a complete monopoly on aluminum despite the existence of a highly competitive market in secondary or reclaimed aluminum (made from scrap) accounting for about one-third of the total aluminum used for fabrication. He justified this conclusion on the grounds that all secondary aluminum derives ultimately from primary aluminum produced earlier and hence that the Aluminum Company through its control of the output of primary aluminum indirectly controlled the quantity of scrap available.

            Evaluate the economic validity of this argument. To simplify your analysis assume that a single firm, say the Aluminum Company of America, has a complete monopoly of primary aluminum; that aluminum for fabrication comes from primary aluminum and secondary aluminum; and that primary and secondary aluminum are perfect substitutes. Indicate in detail how to determine the optimum price for the Aluminum Company to charge and the optimum output for it to produce if (a) the secondary aluminum is refined and sold by a large number of firms under competitive conditions; (b) it has a complete monopoly of secondary aluminum as well.

            Hand’s conclusion presumably is that the price of aluminum would be the same in cases (a) and (b). Is he correct? If not, would it be higher in case (b) than in case (a)? Lower?

2. It is widely argued that entrepreneurs engaged in a number of different activities somehow have a “competitive advantage” over entrepreneurs engaged only in one even if no technical economies are achieved by combining the activities. This general argument and the supposed advantage take many different forms: sometimes it is that one activity provides a “guaranteed” market for another activity; sometimes that one activity provides financing or capital for another; sometimes that a monopoly in one line confers an advantage in another. A recent example of this reasoning is contained in a report by The Chicago Daily news financial columnist on November 20, 1951 that Sears-Roebuck had completed an arrangement with Kaiser-Frazer to market an automobile under the name of “Allstate.” The columnist commented “also there is the Allstate Insurance Company, a wholly owned subsidiary, which would benefit heavily through liability and other policies written in connection with the sales of an Allstate automobile….Some of the gossip around Detroit has been to the effect that the Allstate would have Sears batteries and tires and certain other Sears accessories as original equipment—which would mean more business for these departments of the company.”

(a) The key question is, of course, whether the financial incentive to Sears to market an automobile is greater because it owns the subsidiary companies than it would be if it did not own them. You will find it helpful in answering this question to consider first two intermediate questions: (b) Given that Sears does own the subsidiary companies and that it is going to market an automobile under its name, is it in its own interests to require that the car be equipped with accessories produced by its companies? (c) To require that cars it sells be insured by its own insurance company?

            In answering both questions (a) and (b), consider separately two cases: (1) The subsidiary companies can be regarded as operating under highly competitive conditions; (2) the subsidiary companies can be regarded as having a monopoly of the products they produce. Do the conclusions depend on the assumption made about competitive conditions? Assume throughout that there are no “technical” economies from combining the various activities.

Source:  Hoover Institution Archives. Papers of Milton Friedman. Box 76, Folder 76.9.

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Economics 300A
Final Examination
December 17, 1951

1. (15 points)
   (a) Appraise: “Recent studies of domestic consumption in low-cost municipalities demonstrate that the demand for electric current is highly elastic, expanding rapidly as the cost declines. The national average consumption of the United States was 604 kilowatt-hours in 1933. The average charge to consumers on October 1, 1934, for the whole country is reported as 5.4 cents per kilowatt-hour. In Seattle where the average cost is 2.58 cents, the average consumption is 1,098 kilowatt-hours. In Tacoma, the charge is 1.726 cents and the consumption 1,550. In 26 cities of Ontario, the average charge is 1.45 cents and the consumption 1,780. Finally, in Winnipeg, where the average net charge is only 8 mills per kilowatt-hour the average per capita consumption exceeds 4,000 kilowatt-hours.” (Report of the National Resources Board, December 1, 1934, Government Printing Office, 1934, p. 39.)

(b) Will a specific tax (a tax of a specified number of dollars per physical unit) on a commodity raise its price more or less than an equivalent ad valoremtax (a tax of a specified percentage of the price)? Assume that the commodity is produced and sold under competitive conditions.

2. (15 points) (a) Figure 1 gives the locus of points of tangency between indifference curves and budget lines parallel to ab (and cd). ABCDEFGH is therefore and “expansion path” or curve showing the quantity of X and Y and individual would buy at different incomes and constant relative prices. Fill in the following table with as precise statements as are deducible from Fig. 1 by observation without measurement:

(b) ABCDEF in Figure 2 is the locus of points of tangency between indifference curves and budget lines representing different money prices for X but the same money price of Y and money income (i.e. budget lines like ab and ac rotating about a). Fill in the following table with as precise statements as are deducible from Fig. 2 by observation without measurement.

3. (20 points) “Monopolistic competition robs the old concept of industry (and also the Chamberlinian group) of any theoretical significance…The value of these groupings is only a concrete, empirical one…Which firms shall be included in any one group will have to be decided, not on an a prioribasis, but after an empirical survey of market realities…In the general pure theory of value, the group and the industry are useless concepts…When the study of competition is freed from the narrowing assumptions of pure competition, only two terms remain essential for the analysis: the individual firms, on the one hand; the whole collectivity of competitors on the other.” (Triffin)

(a) Explain why “monopolistic competition robs the old concept of industry…of any theoretical significance.”
(b) Explain the general position summarized in this quotation and discuss it critically.

4. (20 points) Find the mistakes (there are at least six) in the accompanying diagram showing long and short run marginal and average cost curves, and explain the general principle corresponding to each particular mistake.

5. The accompanying diagram showing a set of indifference curves between income and work is part of a diagram given by Boulding in Economic Analysis in his discussion of the effects of various types of direct taxation, and reproduced by Schwartz and Moore in the March 1951 American Economic Review. The latter write, “Given O Q₂Q₅ as a rate of pay, the equilibrium position is P₁ where the rate of pay is equal to the MRS between leisure and income. Let us assume that we are to collect a tax from this individual equal to OL. One method of collecting the tax would be to levy a poll tax, leaving the rate of pay unaltered, as LP₅. Another direct tax would be a proportional income tax represented by OSP₂ which would have the effect of lowering (flattening) the rate of ‘take-home’ pay. To extract the same amount of revenue as the poll tax does, this rate of pay must be tangent to an indifference curve at an intersection with LP₅. Thus P₂Q₂ = OL. Since the rate of ‘take-home’ pay is flatter, P₂ must lie below and to the left of P₅; i.e. less effort is expended and the worker enjoys a smaller net income. More important, his welfare is diminished because he must be on a lower indifference curve…Given the premises of the conventional indifference curve pattern, this must necessarily be true.”

(a):

(1) Why do the indifference curves in the diagram slope positively?
(2) How can you justify their being drawn concave upwards?
(3) The statement that OQ₂Q₅ is “a rate of pay” is of course wrong. OQ₂Q₅ is a line. Reword the statement so it is accurate.
(4) What do the authors mean by MRS?

(b) If we suppose the diagram to stand for a “representative” individual, or one of a society of identical individuals all to be taxed alike, the last sentence in the quotation is false: the authors’ welfare conclusion does not follow from their premises and arguments. Point out the fallacy in the proof.

(c) Under what conditions is the authors’ welfare conclusion valid? Can you give a proof of your statement?

Source:  Hoover Institution Archives. Papers of Milton Friedman. Box 76, Folder 76.9.

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Economics 300B
Winter, 1952
PROBLEM FOR READING PERIOD

Available evidence tentatively indicates that (1) average income of white families living in the same size city is roughly the same in the North and the South; (2) the wage rate of a white worker in any given occupation is higher in the North than in the South for cities of the same size; (3) property income is roughly of equal importance for white families in the North and the South.

For purposes of this question, accept these as correct statements of fact. Can you suggest any way of reconciling the apparent contradiction among them? Presumably, any reconciliation will turn on the larger fraction of negroes and greater discrimination against them in the South than in the North.

Spell out your suggestion in detail, explaining the theoretical links if any between the higher fraction of negroes and greater discrimination, on the one hand, and the indicated results on the other. Indicate how the validity of your suggestion would be tested.

Source:  Hoover Institution Archives. Papers of Milton Friedman. Box 76, Folder 76.10.

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ECONOMICS 300B
Final Examination
March 12, 1952

2. 1. (35 points) Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and state briefly the reason for your answer. It is to be understood that in each question the appropriate “other things” are to be held constant.
      1. The imposition of a minimum wage for labor of type X higher than the preceding wage leads to an increase in the number of laborers of type X employed. It follows that labor of type X is hired under monopsonistic conditions. [True]
      2. Under both competition and monopoly in the product market, marginal value product of a factor to a firm is equal to marginal physical product of the firm times marginal revenue to the firm from the sale of the product. [True]
      3. Marginal productivity analysis shows that, in the absence of monopsony, a laborer gets as a wage his marginal value product. If this analysis is correct, it follows that unions can raise wages in the absence of monopsony only if they either make each worker more efficient, or increase demand for the product, or make the demand for the product more elastic. [False]
      4. The law of variable proportions (or diminishing returns) is contradicted by the fact that agricultural output of this country has increased tremendously despite a decrease in the proportion of the working population on farms. [False]
      5. The rate of interest is equal to the rate of time preference of consumers. [True]
      6. At present levels of operation, three quarters of the total cost of the XYZ railroad is overhead cost that does not vary with traffic, only one quarter is variable cost. It follows that marginal cost is much less than average cost. [False]
      7. The demand curve of an individual firm for a factor of production is identical with its marginal value productivity curve for the same factor of production. [False]
      8. The demand curve of a firm for a factor of production is a meaningless concept if the firm is a monopsonistic purchaser of that factor. [True]
      9. A declining long run supply curve is impossible in a competitive industry. [False]
      10. Marginal factor cost is equal to the price per unit of a factor whenever the product market is competitive. [False]
      11. According to the theory of joint demand, the absolute value of the elasticity of derived demand for a factor of production will be smaller the more inelastic the supply of that factor. [False]
      12. The fact that individuals do not choose occupations solely on the basis of their pecuniary attractiveness helps explain why the supply curve of labor for a particular occupation has an elasticity greater than zero. [True]
      13. If all types of services were used only in fixed proportions, a marginal-productivity theory would be neither necessary nor possible. [False]
      14. Our society is often described as a “profit” economy or “profit-maximizing” economy. The word “profit” is here used in the same sense as in the uncertainty theory of “profit.” [False]
      15. “Profit” as defined in the uncertainty theory of profit is the expected return to any factor assuming uncertainty over and above the guaranteed expected income it can obtain if it assumes no uncertainty. [False]
      16. If one income is higher than another before income tax it will also be higher after a progressive income tax, provided only that the marginal tax never exceeds 100%. It follows that if one accepts the theory that individuals act as if they sought to maximize their income, he must also accept the conclusion that such taxes do not alter individual’s actions and hence are not shifted. [False]

17 and 18. A minimum wage law is repealed. The wage rate of a class of workers hired under competitive conditions was equal to the minimum before repeal and falls after repeal. It follows that:

2. 1. 17. The total wage bill for this class of labor will rise, remain constant, or fall, according as the elasticity of demand for labor of this class is greater than, equal to, or less than unity in absolute value. [True]
      18. The quantity of labor of this class employed will fall, remain constant, or rise according as the elasticity of supply of labor of this class is positive, zero, or negative. [False]
      19. The great technological improvements in the past few decades in the production of synthetic fibers (rayon, nylon, etc.) and associated decline in their relative price has, among other effects, tended to raise the price of meat in general, especially of lamb and mutton. [True]
      20. At the same time, stringent rationing of meat consumption in Great Britain, by tending to offset this effect, has improved the competitive position of the synthetic fiber industry, and so enabled it to expand more than otherwise. [True]
3. (15 points) “The wages of every class of labour tends to be equal to the net product due to the additional labour of the marginal labourer of that class.
   “This doctrine is not a theory of wages: but is a useful part of a theory.” (Marshall)(a) What does Marshall mean by “net product”? [4] By “Marginal labourer”?[4]
   (b) Explain and evaluate the second sentence in the quotation. [7]
4. (15 points) It is frequently argued that a tax on a product imposed at the manufacturing level involves a greater burden on consumers than a tax yielding the same revenue imposed at the retail level because the tax is “pyramided,” i.e., the “margins” of wholesalers and retailers are viewed as given percentages of purchase price and so, it is argued, price will tend to rise not only by the tax but also by the “margins” on the tax.
   Evaluate this argument.
5. (10 points) The price of nylon thread for use in making women’s hosiery was recently lowered drastically when DuPont decided to make much larger quantities available. The resulting decline in the price of hosiery was viewed by at least some manufacturers and retailers as a misfortune and as portending smaller profits for themselves. Were they right? In the short run? In the long run? Justify your answers.
6. (10 points) A subsidy of $X is paid per acre of land devoted to growing soy beans. Will this lead to a rise or to a decline in the yield per acre on land devoted to growing soy beans prior to the introduction of the subsidy? Justify your answer.
7. (15 points)
   (a) What is the Pigou effect?[4] What relevance does it have to the theory of the rate of interest?[4]
   (b) List some economic decisions that would be affected by a change in the rate of interest. Indicate why they would be affected and if possible the direction of the effect. [7]

Source:  Hoover Institution Archives. Papers of Milton Friedman. Box 76, Folder 76.10.

Image Source: Milton Friedman (undated). University of Chicago Photographic Archive, apf1-06230, Special Collections Research Center, University of Chicago Library.