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Chicago Economists Exam Questions

Chicago. Economic Theory Ph.D. Qualifying Exams, 1932-33

In the papers of economist Albert G. Hart at Columbia University there is a folder that contains nearly a complete run of economic theory qualifying exams from the University of Chicago covering the period 1926-1940. I include here the exam from the Spring quarter 1932 and the exam from the Autumn Quarter 1933, though I cannot say whether Hart himself actually took either one of these two theory exams. The previous two postings have field exams (money and banking exam, economic history exam)  that are (i) unique in his papers and (ii) have his handwritten notations, e.g. questions checked and time started and ended for some questions, so we can be very sure those were indeed “his” exams. In several of the theory exams before the Autumn 1933  there are Hart-like checkmarks over the names of economists explicitly mentioned which has led me to conclude that a part of Hart’s personal examination prep was to go over the old theory examinations to identify the economists most likely to make an appearance in his own economic theory exam. The Autumn 1933 exam of this posting has no such checkmarks and would coincide with the quarter he took his money-and-banking exam. In any event today’s postings are still valuable artifacts from the early 1930s Chicago department.

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ECONOMIC THEORY
Written Examination for the Ph.D.

Spring Quarter, 1932

Time: 3 1/2 hours.

Answer seven questions, of which at least three must be in Part I. C. & A. students may substitute question 6, Part II, for any other question.

Part I

  1. Discuss the relationships between the conclusions and assumptions of the neoclassical school[✓], the Weber[✓]-Sombart[✓] school, and the American institutionalists[✓].
  2. Trace the development of the demand concept from Adam Smith to the present, touching on the contributions of J.S. Mill[✓], Cournot[✓], Fleeming Jenkin[✓], Walras[✓], Böhm-Bawerk[✓], and the statistical economists. [(Schultz)]
  3. A producer of cement has a monopoly of the market in the area adjoining his plant, but is an insignificant factor in the rest of the country, where there are many competing producers. He can sell any desired portion of his output in the competitive market at the price there prevailing. Given the price prevailing in the competitive market, the demand schedule in his own monopolized market, his own average cost schedule, and any additional information which may be necessary for the solution of the problem, find the price he should charge in his own market, and the quantities he should sell in each market, to maximize his net revenue.
  4. Answer (a) or (b), but not both.

(a) The final degree of utility curves of A and B for corn (X) and beef (Y) are as follows, the small letters x and y representing the quantities of X and Y consumed by the person indicated by the subscript.

Commodity

Person

X (corn)

Y (beef)

A

fa(xa) = – (3/2)xa + (19/2)

?a(ya) = -(1/2)ya + 6

B

fb(xb) = -(3/8)xb + 5

?b(yb) = – yb + 7

The total market supply of corn is

x = xa + xb = 14

and the total market supply of beef is

y = ya + yb = 8

Without performing any numerical computations, explain how to deduce the combined demand curves of A and B for corn in terms of beef and for beef in terms of corn.

(b) Is there an equilibrium price and output when a commodity is produced by two competing monopolists? Discuss this problem touching on the solutions of Cournot[✓], Edgeworth[✓], Amoroso[✓], and Wicksell[✓].

Part II

  1. Describe the history and status of the real cost theory [✓] of value. [Marx]
  2. Point out the resemblances and the differences between the preconceptions, the methods of analysis, and the conclusions, of Adam Smith and the physiocrates [sic], or of the mercantilists and the physiocrates [sic], or of Malthus and Ricardo.
  3. Give some reasonable objectives for a centrally planned economy in a democratic state; state the grounds of your selection of objectives; indicate and discuss possible lines of procedure for realizing them through price control.
  4. Explain and comment on the following in connection with interest theory; [BB; Hayek; Fisher[?]]

(1)  length of the productive period; (2) underestimate of the future; (3) marginal physical productivity of waiting; (4) marginal abstinence; (5) “evening out the income stream.”

5.  Discuss the significant of variability of the proportions of the factors of production and of variability of the supplies of the productive factors for a marginal productivity theory of distribution.

For C. & A. students only

6.   Discuss the feasibility and merits of inflation in the present stage of the depression.

 

Source: Columbia University Libraries, Manuscript Collections. Albert Gailord Hart Collection. Box 60, folder “Exams: Chicago”.

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ECONOMIC THEORY
Written Examination for the Doctorate

[Part I, Price theory/Microeconomics]
Autumn Quarter, 1933

Time: Three Hours.

Answer all the questions as directed.

1.   (Answer both parts)

A.  Defined or very briefly describe:

(1) Inelastic demand
(2) Elastic demand
(3) Incremental (or marginal) revenue
(4) Perfect competition (in terms of demand elasticity)
(5) Pure profit
(6) Productivity (incremental or marginal of a particular agency or factor)

B.  Is export dumping evidence of domestic monopoly? Explain. Under what conditions does export dumping lead to a lower domestic price in the exporting country?

2.   (Answer either A or B)

A.  State briefly the doctrine of market price and natural price of the early classical economists; contrast this with Marshall’s analysis of long-run and short on price, and give your own view of the correct classification of viewpoints with respect to time.

B. State and critically discuss the classical doctrine of productive and unproductive labor, and in view of the issues raised formulate a correct definition of production in economics.

3.  The theory of marginal utility: its origin, principal forms or interpretations, your own view of its meaning and use in price theory, and the critical appraisal of its validity. Consider especially the relations between the use of the principle as an explanatory concept and as a premise for the discussion of social policy.

4.  (Answer either A or B)

A.  Discuss the effects of establishing by legal action be minimum wage above the wage actually received by, say, one-fourths of the workers actually employed: (a) under conditions of prosperity with approximately full employment; (b) under depression conditions with a large volume of unemployment.

B.  Criticized the view that industry fails to distribute sufficient purchasing power to buy its product, resulting in economic on balance.

5. Show graphically the effect of lowering the tariff on sugar. (Assumed domestic and foreign demand and supply curves given, and neglect any disturbances in the balance of international payments.)

6. Briefly characterize and evaluate comparatively what you considered the significant “approaches” or methodologies in economic science. (The following are to be taken as suggestive catch-words: classical, inductive, institutional, historical, deductive, price theory, sociological, socialistic, control.) We are possible, cite examples of the different tendencies in the history of economic thought from the Greeks to the present.

 

PART II
MONETARY AND CYCLE THEORY

Written Examination for the Ph.D.
Autumn Quarter, 1933

Time: 2 hours

Answer four questions, including the first two.

  1. State the classical doctrine of international gold flows and price levels and discuss some recent criticism of this doctrine.
  2. “The primary cause of business depression is the rigidities of the price structure.”  “Through their alternating contraction and expansion of the circulating medium the banks are responsible for the wide swings in industrial activity.” Discuss these statements.
  3. Discuss the theoretical short-comings involved in a policy on the part of our federal government of progressively bidding up the price of gold in foreign markets.
  4. If business recovery came without the assistance of governmental inflation it would be accompanied by an expansion of the circulating medium as a result of the lending operations of the commercial banks. What significant similarities and differences are there between such expansion and (a) government borrowing from the banks in order to finance public works, (b) outright “greenbackism”?
  5. It has been argued that in as much as the demand for capital goods is a derived demand it follows that any voluntary saving will necessarily result in some degree of unemployment. That is to say, the savings will reduce the demand for consumers’ goods, thus reducing the demand for capital goods, and consequently not all the savings will be borrowed; hence unemployment. But the commercial banks, through their power to create circulating medium, make it possible for entrepreneurs to obtain the funds with which to create capital goods without the reduction in consumer demand which comes with saving. Hence the banks furnish a means of escape from the dilemma. Discuss.

Source: Columbia University Libraries, Manuscript Collections. Albert Gailord Hart Collection. Box 60, folder “Exams: Chicago”.

Image Source:  Social Science Research Building (Lecture Hall 1). University of Chicago Photographic Archive, apf2-07482, Special Collections Research Center, University of Chicago Library.

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Chicago Economists Exam Questions

Chicago. Economic History, Ph.D. qualifying exam, 1933

The previous posting was a transcription of the examination questions for the Ph.D. qualifying exam in money-and-banking (a.k.a. financial organization) at Chicago in 1933. This posting gives us the analogous exam for the field Economic History which tested both U.S. and Western European economic history equally. Bracketed checkmarks have been included for the questions that the economist A. G. Hart explicitly checked himself.  It seems  unlikely that Hart did not answer two of the last three questions of Group II, but until someone finds the typed copy of his exam (see introduction to previous posting, link above), we won’t know.

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ECONOMIC HISTORY
Written Examination for the Ph.D.

[University of Chicago]
Summer Quarter, 1933

Time: 4 hours

Divide your time equally between Group I and Group II.

Where suitable, answers in outline form are preferable and will save time. Read the instructions and questions carefully.

Group I

Answer question 1 and 3 others. Time, 2 hours.

  1. [✓] What reasons can you suggest to explain why the per capita money income in the United States around the first of the twentieth century was so much higher than that in the United Kingdom?
  2. [✓] Explain how economic conditions in the colonies reacted upon the transplanting of English institutions, political, social and economic, in the colonies.
  3. Describe the chief laws governing the disposition of the public domain since 1800 and give a critical estimate of the results of this legislation.
  4. [✓] Enumerate the various ways in which our ideal of democracy (in the broad sense) has reacted upon our economic history.
  5. [✓] Outline and explain the history of our merchant marine since 1789.
  6. Trace the evolution of the financial institutions upon which agriculture had to depend for its credit since about 1820, giving a critical estimate of the adequacy of these facilities at different periods.

Group II

Answer question 1 and 3 others. Time, 2 hours

  1. [✓] Make an outline or list of the main changes in economic institutions from 12th-century West-Europe to the World War. Briefly compare the conditions of at the later date with economic organization at the height of “classical” (Greco-Roman) civilization.
  2. [✓] Discuss in detail the manner in which the rising prices during the 16th century may have affected industrial development in England, France and the Belgian provinces? What comfort can advocate of “controlled inflation” today derived from the monetary history of the 16th century in these three countries?
  3. Compare the agrarian history of Italy in the first and second centuries A.D. With that of northern France in the twelfth and thirteenth centuries A.D. To what extent, if any, can the differences be explained by the differences in the natural resources of the two countries?
  4. Trace the history of thought in connection with any one of the following three subjects from the earliest times down to the present: (a) the influence of climate upon civilization; (b) The quantity theory of money; (c) The influence of religion upon the rise of capitalism.
  5. Selects some topic in economic history which you would be interested in investigating. Tell how you would go about obtaining the material. What sort of historical criticism would you apply to the material?

 Source: Columbia University Libraries, Manuscript Collections. Albert Gailord Hart Collection. Box 60, folder “Exams: CHI QUALIFYING”.

Image Source:  Social Science Research Building (Lecture Hall 2). University of Chicago Photographic Archive, apf2-07483, Special Collections Research Center, University of Chicago Library.

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Chicago Economists Exam Questions

Chicago. Money and Banking Ph.D. qualifying exam, 1933

A. G. Hart’s education and career covered the big three economics departments of his day (Harvard, Chicago and Columbia). For my research on the history of economics education his papers constitute a particularly rich vein of material. In today’s posting I have transcribed the questions for his “qualifying examination” in money-and-finance at the University of Chicago. Bracketed checkmarks indicate the questions Hart chose to answer (the checkmarks are presumably his). In his memo of February 1985 (Columbia University, A. G. Hart papers: Box 60, Folder “Sec I Notes on teaching materials, Learning”) Hart wrote that his files include “answers to ‘qualifying examinations’ in microeconomics, money-and-finance, and economics history” to which he added the following footnote: “I was allowed to write these [qualifying] exams with aid of a typewriter, so that I was able to keep a legible copy. I ducked the qualifying exam in statistics (in which for that date I was very well trained) because I disapproved of the focus of previous exams upon minor technicalities—hence I exploited the loophole which made ‘financial organization’ a separate field even though in principle the ‘theory’ exam included monetary economics.” I must have missed his typed examination answers (or they were lost or misfiled). Perhaps someone else will locate them and post a comment here some day…

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THE FINANCIAL SYSTEM AND FINANCIAL ADMINISTRATION

Written Examination for the Ph. D. Degree
[University of Chicago]
Autumn Quarter, 1933

 

Time: 4 hours.

 

Write on 7 questions, including the first two in Part I and any two in Part II.

Part I

  1. [✓] Assume a large deposit of new gold in a member bank in the United States. Show the precise manner in which this deposit would result in an expansion of the circulating medium, and the approximate extent of such expansion. Develop in terms of the following topics: (a) a single bank; (b) the banking system; (c) drain of cash into circulation.
  2. [✓] Discuss the respective merits and limitations of the following as alternative methods of contributing to sustained recovery from the current depression: (a) the program of construction of public works financed by sale of bonds to banks; (b) federal unemployment benefits financed by sale of bonds to banks; (c) open market purchase of bonds by the Federal Reserve banks.
  3. To what extent have weaknesses in our banking system been responsible for the bank failures of the last 13 years[?] Have these weaknesses been remedied by recent legislation? If not, what changes would you recommend?
  4. [✓] “A world that was striving to maintain the currency system with the wider ambit than its banking system, its tariff system, and its wage system, witnessed the smash of them all – and blamed it on gold. Now that the full extent of the chaos is realized[,] one might wonder why the whole mechanism did not break down sooner in view of the well-nigh universal refusal to observe the rules of the game (gold standard).” What is the significance of the author’s first sentence? How would you state the “rules of the game”?
  5. [✓] Discuss the theoretical short-comings involved in a policy on the part of our federal government of progressively bidding up the dollar price of gold in foreign markets.
  6. Do the following experiences with paper money throw any light on the possible outcome of the present monetary and fiscal situation in the United States? The assignats, the period of the restriction in England, the Greenback Era, the post-world-war experiences in Europe.
  7. [✓] State and evaluate the argument that “maldistribution” of income is the cause of recurrent business depressions.

 

Part II

 

  1. [✓] It is alleged that the investment market has “dried up” because investors and bankers are uncertain of the future value of the dollar and because of the paralysis of investment banking caused by the “securities law.” Do you consider the allegations sound? Why or why not?
  2. [✓] What industries would be likely to profit most from a return to the 1926 price level? What industries least? Defend your answer. Be careful to state any important assumptions. Classify industries as you please.
  3. Assume you are treasurer of an automobile manufacturing corporation having a $5,000,000 bond maturity on January 1, 1934. What factors would you consider in planning to meet this maturity and why would you consider each of them?

 

Source: Columbia University Libraries, Manuscript Collections. Albert Gailord Hart Collection. Box 60; Folder “Sec 2 Ec 230 1933 Chicago Money (Summer course)”.

Image Source:  Social Science Research Building (Entrance, North 3). University of Chicago Photographic Archive, apf2-07466, Special Collections Research Center, University of Chicago Library.

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Exam Questions Harvard Suggested Reading Syllabus

Harvard. Business Cycles and Economic Forecasting. Schumpeter, 1948

Business Cycles and Economic Forecasting was a two semester graduate course at Harvard. The fall term (Economics 245a) was taught by Joseph Schumpeter and the spring term (Economics 245b) was jointly taught by Assistant Professor Richard Goodwin and Professor Gottfried Haberler. This posting includes a transcription of a carbon copy of the final exam questions for Schumpeter’s course along with his course reading list for the fall term of 1948. An undated note to the veteran’s office that identifies books that veterans be reimbursed for purchasing is included below.

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1948-49
Economics 245a
[Professor Joseph Schumpeter]
Fall Term

Work in this course will concentrate on a number of selected topics in business-cycle analysis and forecasting rather than aim at covering the entire field systematically. As much opportunity as possible will be given for discussion of, and essays on, individual problems. Some knowledge of advanced theory and advanced statistics is necessary in order to reap the full benefit from this course: providual [sic, individual] needs will be taken care of in consultation.

I.

a. Students are expected to be, or to make themselves, familiar with the two following standard works:

Haberler, Prosperity and Depression, 1941.
Pigou, Industrial Fluctuations, 1929.

b. There are a number of useful textbooks that less advanced students may usefully consult for survey purposes: E. C. Bratt, Business Cycles and Forecasting, 3rd ed., 1948, is recommended (not “assigned”).

c. Attention is called to Readings in Business-Cycle Theory (Vol. II of the Blakiston Series of Republished Articles on Economics, 1944. See especially Nos. 2, 4, 10, 12, 14, 21 and Bibliography by H. M. Somers).
William Fellner, Employment Theory and Business Cycles in A Survey of Contemporary Economics (ed. H. S. Ellis, Blakiston, 1948)

d. Perusal of The Federal Reserve Board’s Chart Books I and II is strongly recommended, and so is the study of

e. E. Frickey, Economic Fluctuations in the United States (Harvard Economic Studies, 73) which should be supplemented by
E. Frickey, Production in the United States, 1860-1914 (Harvard Economic Studies, 82)

[f. This time, the program of the course does not include Business Cycles (National Bureau of Economic Research, 1946). Owing to its importance, the book is nevertheless mentioned here for the benefit of students who propose to specialize in business cycles.]

 

II. Further suggestions with reference to topics that will be dealt with in the course.

a. Books:

J. G. Stigler, Trends in Output and Employment (N. B. E. R., 1947)
J. M. Clark, Strategic Factors in Business Cycles, 193
A. H. Hansen, Economic Policy and Full Employment, 1947
A. H. Hansen, Fiscal Policy and the Business Cycle, 1941.

b. Articles:

(1) S. H. Slichter, The Period 1919-36 in its Significance for Business-Cycle Theory, Review of Economic Statistics, 1937.
H. L. Beales, The Great Depression, Economic History Review, October, 1934.

(2) M. Kalecki, A Theory of the Business Cycle, Review of Economic Studies, February, 1937.
L. A. Metzler, Business Cycles and the Modern Theory of Employment, American Economic Review, June, 1946.
N. Kaldor, A Model of the Trade Cycle, Economic Journal, March, 1940.

(3) G. Haberler, Some Reflections on the Present Situation of Business-Cycle Theory, Review of Economic Statistics, 1936.
Hansen, Boddy, and Langum, Recent Trends in Business-Cycle Literature, Review of Economic Statistics, 1936.
H. S. Ellis, Notes on Recent Business-Cycle Literature, Review of Economic Statistics, 1938.
Jacob Marschak, A Cross Section Of Business-Cycle Discussion, American Economic Review, June, 1945.
J. Tinbergen, Critical Remarks on Some Business-Cycle Theories, Econometrica, April, 1942
T. Koopmans, The Logic of Econometric Business-Cycle Research, Journal of Political Economy, 1941.

(4) J. Einarsen, Reinvestment Cycles, Review of Economic Statistics, 1938.
W. Isard, A Neglected Cycle: The Transport-Building Cycle, Review of Economic Statistics, 1942.
O. Morgenstern, On the International Spread of Business Cycles, Journal of Political Economy, 1943.
Irving Fisher, The Debt-Deflation Theory of Great Depressions, Econometrica, 1933.

 

Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003 (HUC 8522.2.1), Box 4, Folder “Economics, 1948-1949 (2 of 2)”.

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[Final Examination]

HARVARD UNIVERSITY
Economics 245 A

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

  1. Describe the various underconsumption theories of depressions and discuss their explanatory value.
  2. Explain the mechanism of inventory cycles and state your opinion about the importance of the phenomenon.
  3. Prolonged periods of prosperity and depression have been traced to expansions and contractions in gold productions. Analyze the action of increases or decreases in gold stocks upon the economic process of the periods in which they occurred and show how they could, or could not, have produced the cycles or sequences of cycles attributed to them.
  4. Examine the validity of harvest theories of business cycles.
  5. Accepting, for the sake of argument, the innovation theory of cycles, how would you expect money wages and real wages to behave in the course of the cyclical phases?

Final, January 1949

 

Source: Harvard University Archives. Joseph Schumpeter Papers (HUG(FP)-4.62). Lecture Notes Box 2, Folder “Business Cycle Lecture notes Fall 1948”.

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To the Veteran’s Office, with apologies for delay: [undated]

Note: Economics 203 and 245 are advanced courses in which no textbooks are assigned, and the assignments of other books are of the character of advice rather than of strict requirement. However, I mention below books which I do advise students to buy. Most of them are required in other courses.

I. For Economics 203

J. R. Hicks, Value and Distribution [sic, “Capital”], Oxford Press, New edition just out.
A. Marshall, Principles, Macmillan, any edition from 4th to 8th.
Lord Keynes, General Theory of Employment, Interest and Money, Harcourt Brace, 1st edition, 1936.
E. H. Chamberlin, Theory of Monopolistic Competition, Harvard Press, last edition.
Irving Fisher, Theory of Interest, MacMillan, 1930
K. Wicksell, Lectures Vol. I, Routledge, 19334 (if available)

 

II. For Economics 245

Alvin Hansen, Economic Policy and Full Employment, McGraw-Hill
Edwin Frickey: a) Fluctuations, b) Production, both Harvard Press
Burns and Mitchell, Measuring Business Cycles, National Bureau of Economic Research, 1819 Broadway, New York 23, N.Y.
Bratt, Business Cycles, 3rd edition, 1948, (Irwin).
[handwritten addition:] Reading in Bus. Cycles. Blakiston.

Source: Harvard University Archives. Joseph Schumpeter Papers (HUG(FP)-4.62). Lecture Notes Box 2, Folder “Misc course notes 1943-48 (found in Littauer M-5)”.

Image Source: Harvard Album, 1947.

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Exam Questions Harvard Suggested Reading Syllabus

Harvard. Mathematical Economics. Leontief, 1948

There are only marginal differences to be found  from the course outline for 1941-42 and 1942-43, e.g. “Time lags and sequences” instead of “Cobweb Model” plus addition of Mosak (General Equilbrium Theory in International Trade) and Samuelson (Foundations of Economic Analysis) to the course bibliography. We also see that Marshall’s Mathematical Appendix was a “new” assignment for the reading period.  Midterm and Final exam questions are included in this posting.

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[Course Outline, Leontief]

Economics 4a
Spring Term, 1948

Introduction to the Mathematical Treatment of Economic Theory

  1. Introductory remarks
    Profit function
    Maximizing profits
  2. Cost functions: Total costs, fixed costs, variable costs, average costs, marginal costs, increasing and decreasing marginal costs.
    Minimizing average total and average variable costs
  3. Revenue function
    Price and marginal revenue
    Demand function
    Elasticity and flexibility
  4. Maximizing the net revenue (profits)
    Monopolistic maximum
    Competitive maximum
    Supply function
  5. Joint costs and accounting methods of cost imputation
    Multiple plants
    Price discrimination
  6. Production function
    Marginal productivity
    Increasing and decreasing productivity
    Homogeneous and non-homogeneous production functions
  7. Maximizing net revenue, second method
    Minimizing costs for a fixed output
    Marginal costs and marginal productivity
  8. Introduction to the theory of consumers’ behavior
    Indifference curves and the utility function
  9. Introduction to the theory of the market
    Concept of market equilibrium
    Duopoly, bilateral monopoly
    Pure competition
  10. Time lag and time sequences
  11. Introduction into the theory of general equilibrium

Bibliography:

R. G. D. Allen, Mathematical Analysis for Economists
Evans, Introduction into Mathematical Economics
Antoine Cournot, Researches into the Mathematical Principles of the Theory of Wealth
Jacob L. Mosak, General Equilibrium Theory in International Trade
Paul A. Samuelson, Foundations of Economic Analysis

Reading Period Assignment: Alfred Marshall, Principles of Economics, Mathematical Appendix

 

Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003. HUC 8522.2.1, Box 4, Folders “Economics, 1947-1948 (1 of 2)”.  Copy also in Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.

 

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[Midterm Exam]

Economics 4a
Hour Examination
March 23, 1948

Answer two questions, including Question 3.

1.  Prove that the average costs tend either

(a) toward equality with the marginal costs, or
(b) toward infinity

as the output of an enterprise is reduced toward zero.

2. Describe the relationship between the cost curve and the supply curve of an enterprise.

3.  An industrial enterprise produces jointly two kinds of outputs, X and Y and uses one kind of input, Z. Given

(a)  the production function z = f(x,y), where z, x and y are quantities of Z, X and Y and
(b)  the prices Pz, Px and Py of Z, X, and Y

derive the equations the solution of which would determine the most profitable input-output combination. Don’t forget the secondary conditions.

 

Source: Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.

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[Final Exam]

1947-48
HARVARD UNIVERSITY
ECONOMICS 4a

Please write legibly

Answer four questions including question 6.

  1. Show how a change in the magnitude of the fixed costs would affect the supply curve of a profit-maximizing enterprise selling its product on a competitive market.
  2. Given:

      The production function,

x = yz2

where x is the quantity of output, and y and z represent the amounts of two different inputs purchased at the fixed prices py and pz respectively,

Derive:

            The total cost curve of the enterprise. (A total cost curve represents the functional relationship between various outputs and the smallest total costs at which they can be produced.)

  1. A monopolistic producer sells his output in two separate markets. His cost curve is:

C = K + Q

where C represents the total cost, Q the total output, and K a positive constant. The demand curves in the two markets are:

p1 = A – q1

p2 = B – q2,

p1, p2 and q1, q2 represent the prices charged and quantities demanded in the two markets respectively. A and B are positive constants.

What prices would the monopolist charge in the two markets in order to maximize his total net revenue?

  1. A worker maximizes his utility function:

u(c, l)

where c represents his consumption and l the number of hours worked. The hourly wage rate is w dollars.

Determine the equation showing how many hours of labor, l, the worker will supply at any given wage rate, w. Analyze the conditions under which an increase in the wage rate might reduce the number of hours worked.

  1. Discuss the problem of measurability of utility.
  2. A consumer receives a fixed income y1 in “year I” and a fixed income y2 in “year II.” He is free to augment his consumption during year I by borrowing money from the outside on condition that it be paid back with interest out of the income of year II. He can also spend during the first year less than his total income y1. The resulting savings plus the accrued interest will be added in this case to the second year’s consumption. No transfer of any savings beyond the second year and no borrowing against the income of the later years is allowed.

Given:

(a) the utility function,

u(x1, x2)

to be maximized where x1 and x2 stand for the consumption of the first and the second year, and

(b)  the rate of interest i

Derive:

(1) the equations which determine the optimum amount of savings (or borrowings) s;

(2) the formula showing the effect of an infinitesimal change in the rate of interest i on the amount of savings (or borrowings) Interpret the meaning of such a formula.

 

Final. May, 1948.

Source: Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.

Image Source: Harvard Album, 1947.

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Exam Questions Harvard Undergraduate

Harvard. Labor Economics and Social Reform Divisional Exam, 1939

This posting offers the special examination questions for labor economics and social reform. Socialist themes can be seen to have played a much greater role in 1939 than later in the 20th century.

Concentrators in Economics will have to pass in the spring their Junior year a general examination on the department of Economics, and in the spring of their Senior year an examination correlating Economics with either History or Government (this correlating exam may be abolished by 1942), and a third one on the student’s special field, which is chosen from a list of eleven, including economic theory, economic history, money and banking, industry, public utilities, public finance, labor problems, international economics, policies and agriculture.
Courses in allied fields, including Philosophy, Mathematics, History, Government, and Sociology, are suggested by the department for each of the special fields. In addition, Geography 1 is recommended in connection with international policies or agriculture.
[Source: Harvard Crimson, May 31, 1938]

A printed copy of questions for twelve A.B. examinations in economics at Harvard for the academic year 1938-39 can be found in the Lloyd A. Metzler papers at Duke’s Economists’ Papers Project. 

Economic Theory,
Economic History Since 1750,
Money and Finance,
Market Organization and Control,
Labor Economics and Social Reform.

  • One of the Six Correlation Examinations given to Honors Candidates. (May 12, 1939; 3 hours)

Economic History of Western Europe since 1750,
American Economic History,
History of Political and Economic Thought,
Public Administration and Finance,
Government Regulation of Industry,
Mathematical Economic Theory.

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If you find this posting interesting, here is the complete list of “artifacts” from the history of economics I have assembled. You can subscribe to Economics in the Rear-View Mirror below. There is also an opportunity for comment following each posting….

 

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DIVISION OF HISTORY, GOVERNMENT, AND ECONOMICS

DIVISION SPECIAL EXAMINATION
Labor Economics and Social Reform

(Three hours)

 

PART I
(About one hour)

  1. Write an essay on one of the following topics:

(a) wage theory and collective bargaining,
(b) the functions and ideal qualifications of labor-leaders in present-day America, and your appraisals of several of the men now prominent in this capacity,
(c) the rights and duties of labor and employers,
(d) mobility of labor and the national income and its distribution,
(e) the essentials of an adequate, sound, and feasible program for social security,
(f) the possibilities, methods, and probable results of several types of governmental action to lessen inequalities in the distribution of income,
(g) could a socialist society be a liberal and democratic society?
(h) is there any socialism in German National Socialism?
(i) class-struggle in the United States,
(j) the effects of differences of nationality, race, and religion among American workers on the American labor movement,
(k) the effects of capitalism, and the possible effects of socialism, on population growth,
(l) the role of Marxism in the labor movement, in Europe and in America.

Part II
(About one hour)

Answer two questions. Candidates for honors must answer one starred question.

  1. (*) “The industrial system of the ‘machine age’ can give the working population reasonably full employment and high wages only in the periods during which a high rate of technical and economic progress is maintained.”
  2. (*) Discuss the effects upon each other of phases of the business cycle and trade union policies, and the possibilities of the latter as a means of mitigating the cycle.
  3. Discuss legal limitation of hours of work by individual state with respect to (a) questions of constitutionality and (b) possible economic consequences.
  4. Discuss the merits of the proposal for a government-guaranteed “annual wage” in the building trades.
  5. (*) Explain and discuss the main economic problems created in a society by the effects of the declining birth-rate on the distribution of the population among different age-groups.
  6. (*) “The confident belief of reformers bent on equalizing incomes, that inequalities of economic success are the fault of society and not the result of differences of innate ability, cannot be justified in the face of the relevant evidence and results of common-sense reasoning.”
  7. Describe the principal features of the development of workmen’s compensation in the United States or in one European country.
  8. Discuss the achievements and effects of the P. W. A. or of the W. P. A.
  9. (*) “The organization and mechanism of the socialist economy is almost identical with that of monopolistic corporate capitalism. It is the results which would differ.”
  10. (*) If a socialist society gave all its members either equal incomes, or incomes proportioned to their needs or to their sacrifices rather than to their productive contributions, do you think that its policy in this respect would interfere with attainment of the most efficient allocation and use of all labor resources? Explain.
  11. “It is evident that mankind can neither stand pat with the aging Herbert Spencer, nor move on, except to its ruin, with the young men in colored shirts; it’s only hope lies in the creation of a liberal capitalism.”
  12. Explain and support your opinion of the view that in this country the Communists and all “agitators” on the far-left are unlikely to obtain any ends of their own and are likely, instead, to goad or frighten the business men into setting up a regime of American fascism.

 

Part III
(About one hour)

Answer two questions.

  1. “The trade union seems to be the only institution which can prepare us for, or aid us in, social change.”
  2. “The labor movement owes the support of the rank-and-file of the workers who join it, much less to intelligent pursuit of their own economic interests by the latter as individuals, than to their emotional capacities for blind devotion to an ideology and fighting cause which is to them a class religion.”
  3. Compare the functions of trade unions under capitalism with the functions they might have in a socialist society.
  4. In what order of importance do you rank the following objectives of social reform for the benefit of labor: higher real wages; full and steady employment and general security; “industrial democracy” or participation by the workers in the “control” of industry? – Do you think all three objectives are mutually consistent? Explain.
  5. “The goal of intelligent social reform is neither ‘freedom’ of the businessmen to do as they please, nor of government ‘control’ of them reflecting merely the opposing interests and moral sentiments of other people; but is the co-operation of all citizens under expert guidance based on scientific knowledge of economic geography, of our industrial technology and its possibilities, and of the needs and abilities of all sectors of the population.”
  6. What is to be learned from the experience of N. R. A. in the United States and of the Front Populaire in France about the possibility of increasing real wages by raising money wages?
  7. “The increasing organization of interest groups and the resurgent resurgence of mercantilist state regulation of international and domestic markets promise an end of the elaborate economic organization and division of labor and an end of political freedom as well.”
  8. “The traditional view has been that it is consumers who suffer the chief losses from monopoly, but the fact is that the principle losses fall on labor.”
  9. What should be the attitude of consistent Communists in this country at the present time toward such popular economic and monetary theories as those of the advocates of the Townsend Plan? Explain.

May 10, 1939.

 

Source: David M. Rubenstein Rare Book & Manuscript Library, Duke University. Lloyd A. Metzler Papers, Box 7; [Harvard University], Division of History, Government and Economics, Division Examinations for the Degree of A.B., 1938-39.

 

Categories
Columbia Exam Questions Syllabus Uncategorized

Columbia. Junior Year Political Economy. Mayo-Smith, 1880

Yesterday while trawling through the Hathitrust digital library, I came across a collection published in 1882, Examination Papers Used During the Years 1877-1882 in Harvard, Yale, Columbia, Cornell, Amherst and Williams Colleges. (The link takes you to the download page at archive.org)

Hoping for some political economic gold, I paged through the collection that appeared mostly focused on entrance examinations for Latin, Greek, mathematics etc., but eventually I stumbled upon a single examination in political economy for a junior year course (1880) at Columbia College.

The last question of that exam explicitly quotes from the course textbook so I went over to Google Books and searched the phrase “to secure a delusive benefit to individuals”. Sure enough, I could identify the textbook in question as the Manual of Political Economy for Schools and Colleges (3rd ed. 1876) by James Edwin Thorold Rogers. 

Now drunk on Google Books power, I text-searched Rogers’ Manual to locate the pages for answers to all the questions on the 1880 exam. You will find the corresponding page numbers in square brackets following the questions transcribed below…You’re welcome.

The course was taught by Richmond Mayo-Smith as seen in the Columbia College Handbook of Information 1880. I have included descriptive information about the junior and senior classes in history and political economy found there.

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[From the Columbia College Handbook of Information 1880]

SCHOOL OF POLITICAL SCIENCE.

PROFESSORS

John W. Burgess, A. M.,
Constitutional and International History and Law		 Richmond M. Smith, A.M.,
Political Economy and Social Science (Adjunct).
Archibald Alexander, A.M., Ph.D.,
Philosophy (Adjunct).

OTHER OFFICERS

E. Munroe Smith, LL.B., J.U.D:,
Lecturer on the Roman Law		 Clifford R. Bateman, LL.B.,
Lecturer on Administrative Law.

[…]

HISTORY, POLITICAL SCIENCE, AND INTERNATIONAL LAW.

SOPHOMORE CLASS.

1ST TERM. —German History.
2D TERM.—French History.

JUNIOR CLASS.

1ST TERM—English History.
2D TERM—Political Economy.

SENIOR CLASS.

1ST TERM—Constitutional History of the United States.
2D TERM—Constitutional Law of the United States.
ELECTIVE BOTH TERMS—Political Economy

 

History.—During Sophomore and the first half of Junior year the course in history occupies two hours per week. Some text-book is used, usually those of Freeman’s Historical course for German and French history, and Green’s Short History of the English People for English history.

The instruction to the Senior Class occupies also two hours per week throughout the year, and embraces the following subjects :

I. Character and Constitution of the Colonial Governments in North America; their relation to the English Crown and Parliament; and their history to the Declaration of Independence;

II. Character and Constitution of the Continental Congress as a Revolutionary Government; its relation to the State governments and to the people of the States as a central government ; and the history of its supersedure by the Confederate form.

III. Character and Constitution of the Confederacy as a central authority ; its relation to State governments and to the individual; the historical consequence of its defects and weaknesses, and its final supersedure by the Federal form.

IV. History of the Formation and Adoption of the Federal Constitution; nature and powers of the government which it established; its relation to the State governments and the individual citizen.

V. Interpretation of the Provisions of the Federal Constitution.

VI. History of the Development of the Federal Constitution from its adoption to the present time.

The text and reference books used in connection with this course are: Hildreth, History of the United States; Bancroft, History of the United States; Curtis, History of the Constitution; The Federalist; Story, Constitutional Law; Pomeroy, Constitutional Law; Von Holst, Constitution and Democracy in the United States; Benton, Thirty Years’ View; Jennings, Eighty Years of Republican Government in the United States; Fisher, Trial of the Constitution; Decisions of the United States Supreme Court upon all constitutional questions.

 

Political Economy—There are two courses in Political Economy. During the second term of Junior year it is required from all students of that class. A systematic outline of the science is given, generally with the use of a text-book, either Fawcett’s or Rogers’s Manual of Political Economy.

[Fawcett, Henry. Manual of Political Economy. 1st ed., 1863; 2nd ed., 1865; 3rd ed., 1869; 4th ed., revised and enlarged 1874; 5th ed., revised and enlarged 1876; 6th ed., 1883;  7th ed., 1888;  8th ed., 1907.

Rogers, James Edwin Thorold. A Manual of Political Economy for Schools and Colleges. First Edition, 1868; Second edition, revised, 1869; Third edition revised, 1876.]

Political Economy may be elected by the students of the Senior Class, two hours per week throughout the year. Instruction is given by lectures on the following topics:

Systems of Land Tenure, past and present, in different countries, and their economic and social effects; Science of Finance, including a consideration of Money, Paper Money, Banking, and Taxation; Financial History and present situation of England, Germany, France, and the United States. All these topics are treated historically as well as critically; and with reference to the economic development in the History of Civilization.

Three or four theses on topics assigned by the professor are required from students of this class, To furnish these students with facilities for such work, besides the books in the college library, a special library of works in the department of Political Economy has been purchased and is for the exclusive use of the students of this class.

 

Source: Columbia College. Handbook of Information as to the Course of Instruction, etc., etc. New York: 1880, pp. x, 41-43.

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[Examination Questions in Political Economy 1880]

COLUMBIA COLLEGE
POLITICAL ECONOMY

JUNIOR CLASS, 1880.

[Page references to Rogers’ Manual of Political Economy, 3rd ed. 1876]

  1. Give a history of the English Poor Laws. [p. 121 ff.]
  2. What do you mean by Co-operation? What are the supposed advantages to the laborer? Explain the system of the Rochdale Equitable Pioneers [pp. 135-137] and of the Schultze-Delitsch Credit-Banks [p. 106-109].
  3. What determines the rate of wages of labor, and what effect does the customary food of laborers have on their wages? [p. 65]
  4. Explain the following sentence: “It will be clear that the machinery of a Trade’s Union cannot increase wages by depressing the profits of capital.” [p. 90]
  5. Explain and illustrate the following: “Banks of issue find it possible to circulate a far larger amount of paper than the gold on which the paper is based.” What effect does the abstraction of gold have in such a case? [pp. 43 ff.]
  6. What is meant by an income tax; on what part of the income should it be levied and why? [pp. 278-281]
  7. Explain the origin of the Irish cottier system of land tenure, its evils and the proposed remedy. [pp. 175 ff.]
  8. Explain the following sentences from the text book:
    “It (Protection) inflicts actual suffering or inconvenience on the public in order to secure a delusive benefit to individuals.” “It will be clear also that the Protection cannot stimulate general industry.” “In fact, whenever it (the state) protects particular kinds of labor it diminishes capital.” “Every country enjoys a natural protection to its manufactures.” [pp. 234-235]

 

Source: Harry Thurston Peck (ed.), Examination Papers Used During the Years 1877-1882 in Harvard, Yale, Columbia, Cornell, Amherst and Williams Colleges. New York: Gilliss Brothers, 1882, p. 57-58.

Image Source:  University and their Sons. History, Influence and Characteristics of American Universities with Biographical Sketches and Portraits of Alumni and Recipients of Honorary Degrees. Editor-in-chief, General Joshua L. Chamberlain, LL.D.  Boston: R. Herdon Company.  Vol. 2, 1899, pp. 582.

Categories
Chicago Exam Questions Suggested Reading Syllabus

Chicago. Theory of Income and Employment. Domar, 1948

Jacob Marschak’s course “The Theory of Income and Employment” was taught by the (visiting) assistant professor of economics and research associate in the Cowles Commission, Evsey D. Domar, in the Spring Quarter of 1948. The appointment must have taken place after the Announcements for 1947-1948 were published in May, 1947, so one presumes there was a relatively late change in plans.

For those interested in Domar’s early backstory,  Evsey (Joshua) Domashevitsky arrived in the U.S. on the S.S. Taizo Maru that departed 27 July 1936 from Kobe, Japan and arrived at the port of Los Angeles, California August 16. Domar (“race: Hebrew; nationality: White Russian”) was born April 16, 1914 in Lodz, Poland and last resided in Dairen, Manchuria (now Dalian or Talien, China) before he left for the U.S. He worked his way through UCLA and his graduation photo from the college yearbook graces this posting.

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ECONOMICS 335
THE THEORY OF INCOME AND EMPLOYMENT

Spring, 1948
E. D. Domar

Required Reading List

It is assumed that the students are familiar with the contents of the first 20 chapters of A. P. Lerner’s Economics of Control.

 

PART I.   THE MEASUREMENT OF TOTAL OUTPUT.         March 30 – April 1

Simon Kuznets, National Income and Its Composition, V. I, Ch. 1.
J. R. Hicks and A. G. Hart, The Social Framework of the American Economy, ch. 3, 8, 10-13, 15, 16.
National Planning Association, National Budgets for Full Employment.
Survey of Current Business, National Income Supplement, July, 1947.

 

PART II.   THE ESSENCE OF THE THEORY.    April 3- 28.

J. M. Keynes, The General Theory of Employment, Interest and Money.
A. P. Lerner, Economics of Control, ch. 21-25.
American Economic Association, Readings in Business Cycle Theory, ch. 5-12.
S. E. Harris, editor. The New Economics, ch. 9, 11-15, 19, 33, 36.
Oscar Lange, Price Flexibility and Employment, pp. 1-90.
Milton Friedman, “Lange on Price Flexibility and Employment,” American Economic Review, Sept. 1946 (Reprints in Harper Reserve Room).
Lawrence Klein, The Keynesian Revolution, ch. 3-5.
Gottfried Haberler, Prosperity and Depression, Ch. 8, 13.
A. C. Pigou, “The Classical Stationary State,” The Economic Journal, December 1943.
J. E. Meade and P. W. S. Andrews, “Summary of Replies to Questions on Effects of Interest Rates,” and “A Further Inquiry into the Effects of Rates of Interest,” Oxford Economic Papers, No. 1, 1938 and No. 3, 1940.
Simon Kuznets, “Relation between Capital Goods and Finished Products in the Business Cycle,” in Economic Essays in Honor of Wesley Clair Mitchell.
R. F. Kahn, “The Relation of Home Investment to Unemployment,” Economic Journal, 1931.

 

PART III.   UNDERCONSUMPTION, MATURE ECONOMY, AND CAPITAL ACCUMULATION.        May 4-14.

A. H. Hansen, Fiscal Policy and Business Cycles.
A. H. Hansen, Economic Policy and Full Employment, ch. 15, 16, Appendix B.
E. D. Domar, “Expansion and Employment,” American Economic Review, 1947 (reprints on reserve).
E. D. Domar, “The Problem of Capital Accumulation,” (Mimeographed).
P. M. Sweezy, The Theory of Capitalist Development, ch. 10, 12.
J. A. Schumpeter, Capitalism, Socialism and Democracy, Part II.
G. Terborgh, The Bogey of Economic Maturity.
Readings in Business Cycle Theory, ch. 19-20.

 

PART IV.   POLICY          May 15- June 10.

(in addition to preceding readings)

Board of Governors of the Federal Reserve System, Public Finance and Full Employment, Postwar Economic Studies No. 3, pp. 1-21, 53-68.
A. H. Hansen, Economic Policy and Full Employment, parts IV, V, VI.
M. De Chazeau and others (Committee for Economic Development) Jobs and Markets: How to Prevent Inflation and Depression.
E. F. Burchard and others (Oxford University Institute of Statistics), The Economics of Full Employment.
Mints, Hansen and others. Symposium of Fiscal and Monetary Policy, The Review of Economic Statistics, May 1946.
J. Mosak and Arthur Smithies, “Forecasting Post-War Demand,” Econometrica, 1945.
H. Simons, “Hansen on Fiscal Policy,” The Journal of Political Economy, 1942.
National Budgets for Full Employment
Economic Report of the President, January 1948.
A. P. Lerner and F. D. Graham, Planning and Paying for Full Employment.
M. Friedman, “A Monetary and Fiscal Framework for Economic Stability,” (Mimeographed).
W. H. Beveridge, Full Employment in a Free Society, a general survey, with emphasis on Appendix C.

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Economics 335
Final Examination

June 17, 1948
One hour and fifteen minutes

Answer all questions. They carry equal weights.

  1. Ever since the end of the war, it has been asserted by various authorities that increased production is the best cure against inflation. But it can be also argued that while increased production enlarges the supply of goods, it also generates additional income and therefore demand. So in the end it may or it may not mitigate inflation.
    Analyze this question and try to find the correct answer. The quality and depth of your analysis will count more than its quantity.
  2. “In spite of his claims to the contrary, Keynes did not succeed in proving the possibility of underemployment equilibrium if wages and prices were flexible. That a long period of unemployment could persist as a result of wage and price rigidity we had known long before Keynes.”
    Comment on this statement and show what effects would flexible prices and wages have on elimination of unemployment (in a depression) and stabilization of the price level (in an inflation). Indicate clearly every step in your analysis. What practical recommendations follow from your discussion?
  3. You were employed by the U. S. Bureau of the Budget in 1941 to make an economic forecast and to recommend practical policy measures to prevent both unemployment and inflation in the year 1942, when large war expenditures were expected. Following roughly the method of national budgets (or an equally good alternative one) set up a hypothetical but reasonable numerical model for the year 1942. Show clearly (a) the information you will require; (b) the assumptions you will make; (c) how (a) and (b) are brought together; and (d) policy recommendations you will make. Indicate each step explicitly.
  4. Write for some twenty minutes on any subject covered in the course, but not included in the preceding questions and not studied in your term paper. Make sure you have something worth-while to say.

 

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Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library. Evsey D. Domar Papers, Box 15, Folder: “Macroeconomics, Old Reading Lists”; Box 16, Folder: “Final Exams. Johns Hopkins, Stanford, U of Michigan”.

Image Source: Joshua Domashevitsky (Evsey D. Domar), University of California at Los Angeles, Bruin Life Yearbook/Southern Campus Yearbook, 1939, p. 52. Caption to graduation picture: “Joshua Domashevitsky, A. B./Economics/ Transferred from State College of Law, Manchuria: Foreign Trade Club; Artus, Chancellor of the Exchequer 4.”

Categories
Chicago Exam Questions

Chicago. Economic Theory Exams, A.M. and Ph.D. Summer 1949

The economic theory examination committee at the University of Chicago in the Summer Quarter of 1949  for the A.M. and Ph.D. degrees was made up of F. H. Knight (chair), O. H. Brownlee, M. Friedman, and  L. A. Metzler.  49 students took Part I of the exam (33 were Ph.D. students, 16 were A.M. students, equally divided between economics majors and minors). Part II of the examination was taken by 14 Ph.D. students (no A.M. students).  It does not appear that Knight participated in the grading of Part II however.

Two minor notes: Students were assigned numbers, presumably to assure anonymity with respect to their examiners, but the “unlucky” number 13 was not assigned to anyone. The “grade sheet” for the exams is labelled the “Report on Written Examination” which is similar to the use of the word “report” by the registrar’s office on official University of Chicago transcripts (for this usage, see the Patinkin transcripts).

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ECONOMIC THEORY, Part I
[August 2, 1949]

Written examination for the Ph.D. and A. M. Degrees, Summer Quarter, 1949

Ph.D. candidates: Time: 3½ hours. Answer all questions

A.M. Major candidates: Time: 3 hours. Answer question #2 and two others.

A.M. Minor candidates: Time: 2 hours. Answer question #2 and one other.

 

  1. (a) Discuss and evaluate alternative theories of “Profits” as a distributive share.
    (b) It is frequently said that in a private enterprise economy the producers’ motive is to maximize “profits”. Discuss the meaning of “profits” in this connection in relation to your answer to (a).
  1. Write briefly on the meaning of the capital concept and its importance in interpreting economic growth or change. Relate your discussion to the case of a Crusoe economy and state whether (and if so how) the principles are different for the competitive pecuniary social order.
  1. With reference to federal legislation assuring to every resident in the U.S.A. medical care by the physician and hospital of his choice, free and with no special taxation: Appraise the proposal as to effects upon general welfare, assuming that the alternative is the sale of medical insurance, not subsidized, but with the same distribution of personal income effected by cash “relief”.
  1. Briefly discuss the familiar diagram of a family of short-run cost curves for a firm, with an “envelope” as a long-run curve. State the main “cases” for price-equilibrium under monopoly and under “perfect competition.” Explain why the point of tangency with both curves descending may be such an equilibrium-supply, and particularly why it locates the minimum cost for the corresponding output.
  1. Briefly outline or list the main features of the Ricardian theories of value and of distribution and contrast each point with a “sound” modern view.”

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ECONOMIC THEORY, Part II
[August 4, 1949]

Written examination for the Ph.D. Degree, Summer Quarter, 1949.

Time: 2½ hours.

  1. Assume an economic system in which real expenditure upon goods and services (real consumption, investment, government expense) is a function of real income and the interest-rate; show that the set of values which satisfy the conditions for equilibrium in the commodity market (make real savings and investment equal) need not contain the “full-employment” income level; i.e., that level of real income which would be produced when the quantity of labor supplied equals the quantity demanded, both the labor supply and labor demand being functions of the real wage.
    Evaluate the assumptions of this system on terms of their realism, citing the relevant evidence; and indicate modifications which would result in the inclusion of the “full employment” level of income as one of the values satisfying the condition for equilibrium in the commodity market.
  1. Under the so-called “security-reserve proposal” member banks would be required to keep a supplementary reserve against deposits over and above the reserves they are now required to keep in the form of a deposit with a Federal Reserve Bank. This supplementary reserve could be in the form of government securities.a. What is the main purpose, or purposes, of this proposal?
    b. What effect would it have on the ability of the banks to expand credit, and how?
    c. In the light of present economic conditions, what can you say about the urgency of such a “reform”?
  1. It is a common view today that an equal reduction of both taxes and governmental expenditure would contribute to an increase of the national income or counteract a tendency to depression. State your position and discuss carefully.

Source: Hoover Institution Archives. Milton Friedman Papers, Box 76, Folder 10 “University of Chicago Econ. 300B”.

Categories
Exam Questions Harvard

Harvard. A.B. Honors Degree Examination in Mathematical Economic Theory, 1939

Today’s posting is a transcription of the “correlation examination” questions for mathematical economic theory given at Harvard in May 1939.

A printed copy of questions for twelve A.B. examinations in economics at Harvard for the academic year 1938-39 can be found in the Lloyd A. Metzler papers at Duke’s Economists’ Papers Project. 

Concentrators in Economics will have to pass in the spring their Junior year a general examination on the department of Economics, and in the spring of their Senior year an examination correlating Economics with either History or Government (this correlating exam may be abolished by 1942), and a third one on the student’s special field, which is chosen from a list of eleven, including economic theory, economic history, money and banking, industry, public utilities, public finance, labor problems, international economics, policies and agriculture.
Courses in allied fields, including Philosophy, Mathematics, History, Government, and Sociology, are suggested by the department for each of the special fields. In addition, Geography 1 is recommended in connection with international policies or agriculture.
[Source: Harvard Crimson, May 31, 1938]

Economic Theory,
Economic History Since 1750
Money and Finance,
Market Organization and Control,
Labor Economics and Social Reform.

  • One of the Six Correlation Examinations given to Honors Candidates. (May 12, 1939; 3 hours)

Economic History of Western Europe since 1750,
American Economic History,
History of Political and Economic Thought,
Public Administration and Finance,
Government Regulation of Industry,
 Mathematical Economic Theory.

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If you find this posting interesting, here is the complete list of “artifacts” from the history of economics I have assembled. You can subscribe to Economics in the Rear-View Mirror below. There is also an opportunity for comment following each posting….

_____________________________________

 

DIVISION OF HISTORY, GOVERNMENT, AND ECONOMICS
CORRELATION EXAMINATION

Mathematical Economic Theory

(Three hours)

 

Answer either FOUR or FIVE questions, but not more than THREE from either group. If you answer only FOUR questions, write about one hour on ONE of the questions in Group B and mark your answer “Essay.” This question will be given double weight.

A

  1. A consumer’s indifference map for two goods X and Y is defined by \large\frac{4-\sqrt{y+1}}{x+4}=a
    Draw a graph showing the five indifference curves for the values 2, 3, 4, 5, 6 of the parameter a. Verify that they are of “normal” form.
  2. A business produces an income of $x this year and $y next year, where these values can be varied according to the relation y=1000-\frac{{{x}^{2}}}{250} . Show how \left\{ \left( -\frac{dy}{dx} \right)-1 \right\} can be interpreted as the marginal rate of return over cost. Show that the value of this marginal rate is \frac{x-125}{125} when this year’s income is $x.
  3. The market demand for a good is given by p=\beta -\alpha x . The market is supplied by two duopolists with cost functions {{\pi }_{1}}={{a}_{1}}x_{1}^{2}+{{b}_{1}}{{x}_{1}}+{{c}_{1}} and {{\pi }_{2}}={{a}_{2}}x_{2}^{2}+{{b}_{2}}{{x}_{2}}+{{c}_{2}} . Assuming that the “conjectural variations” are zero, show that the reaction curves are straight lines. Deduce the equilibrium output of each duopolist.
  4. (a) A steel plan is capable of producing x tons per day of a low grade steel and y tons per day of a high grade steel, where y=\frac{40-5s}{10-x} . If the fixed market price of low grade steel is half of that of high grade steel, show that about 5½ tons of low grade steel are produced per day for maximum total revenue.
    (b) The steel producer described in Section (a) monopolizes the sale of both quality steels. If the prices of low and high grade steel are $px and $py per ton, the demands are {{p}_{x}}=20-x and {{p}_{y}}=25-2y . Find an equation giving the output x of low grade steel for maximum total revenue. Show, by a graphical method, that just under 6 tons of this steel are produced per day.
  5. Given the marginal utility equations
    {{x}_{1}}d{{y}_{1}}+{{y}_{1}}d{{x}_{1}}\ge 0 , {{x}_{2}}d{{y}_{2}}+{{y}_{2}}d{{x}_{2}}\ge 0 ,
    for which the indifference curves are the rectangular hyperbolas {{x}_{1}}{{y}_{1}}={{c}_{1}} and {{x}_{2}}{{y}_{2}}={{c}_{2}} , given initial amounts a1, b1, and a2, b2 for the individuals (1) and (2) respectively, show that the equilibrium point for a single price transaction is
    {{x}_{1}}=\frac{{{a}_{1}}+p{{b}_{1}}}{2p} , {{y}_{1}}=\frac{{{a}_{1}}+p{{b}_{1}}}{2p} , where p=\left( \frac{{{b}_{1}}+{{b}_{2}}}{{{a}_{1}}+{{a}_{2}}} \right) .
  6. The demand for tea is {{x}_{1}}=40\frac{{{p}_{2}}}{{{p}_{1}}} and for coffee {{x}_{2}}=10\frac{{{p}_{1}}}{{{p}_{2}}} thousand lbs. per week, where p1 and p2 are the respective prices of tea and coffee in pence per lb. At what relative prices of tea and coffee are the demands equal? Draw a graph to show the shifts of the demand curve for tea when the price of coffee increases from 2s to 2s 6d and to 3s per lb.
  7. The production function is x=A{{a}^{\alpha }}{{b}^{\beta }} , where A, \alpha and \beta are constants. If the factors are increased in proportion, show that the product increases in greater or less proportion according as \left( \alpha +\beta \right)  is greater or less than unity. How is this property shown on a vertical section of the production surface through 0 and a given point on the surface? What is the special property of the case \alpha =1-\beta ?
  8. Examine the utility function u=\frac{x+a}{c-\sqrt{y+b}} , where a, b and c are positive constants, and show that the indifference map is a set of parabolic arcs and of normal form for certain ranges of values of the purchases x and y.
  9. If a{{x}^{2}}+b{{y}^{2}} = constant is the transformation function for two goods X and Y, that the marginal rate of substitution of Y production for X production is \frac{ax}{by} and that the elasticity of substitution is always unity.
  10. A monopolist produces cheap razors and blades at a constant average cost of 2s per razor and 1s per dozen blades. The demand of the market per week is {{x}_{1}}=\frac{10}{{{p}_{1}}{{p}_{2}}} thousand razors and {{x}_{2}}=\frac{20}{{{p}_{1}}{{p}_{2}}} thousand dozen blades when the prices are p1 (shillings per razor) and p2 (shillings per dozen blades). Show that the monopoly prices, fixed jointly, are 4s. per razor and 2s. per dozen blades.

 

B

  1. (a) A radio manufacturer produces x sets per week at a total cost of \$\left( \tfrac{1}{25}{{x}^{2}}+3x+100 \right) . He is a monopolist and the demand of his market is x=75-3p , when the price is $p per set. Show that the maximum net revenue is obtained when about 30 sets are produced per week. What is the monopoly price? Illustrate by drawing an accurate graph.
    (b) In the case of Section (a), a tax of $k per set is imposed by the government. The manufacturer adds the tax to his cost and determines the monopoly output and price under the new conditions. Show that the price increases by rather less than half the tax. Find the decrease in output and monopoly revenue in terms of k.
    Express the receipts from the tax in terms of k and determine the tax for maximum return. Show that the monopoly price increases by about 33 per cent. when this particular tax is imposed.
  2. (a) If u={{x}^{\alpha }}{{y}^{\beta }} is an individual’s utility function for two goods, show that his demands for the goods are x=\frac{\alpha }{\alpha +\beta }\frac{\mu }{{{p}_{x}}} and y=\frac{\beta }{\alpha +\beta }\frac{\mu }{{{p}_{y}}} where px and py are the fixed prices and \mu the individual’s fixed income. Deduct that the elasticity of demand for either good with respect to income or to its price is equal to unity.
    (b) The incomes of an individual in two years are {{x}_{0}} and and {{y}_{0}} his utility function for incomes is u={{x}^{\alpha }}{{y}^{\beta }} . Show that the demand \left( x-{{x}_{0}} \right) for loans this year decreases as the given market rate of interest 100r per cent. increases. Deduce that the individual will not borrow this year at any (positive) rate of interest if {{y}_{0}}<\frac{\beta }{\alpha }{{x}_{0}} .
  3. Discuss this quotation from Chamberlin: “We must conclude that the problems of proportion [among the factors] and of size cannot ordinarily be separated. The goal of the entrepreneur is not to discover the most efficient proportions and then to reproduce these continuously until the most efficient size is secured.”
  4. Discuss this quotation from Douglas: “Since the demand curves for labor and capital tend to approximate and to conform to the respective marginal productivity curves, it follows that an increase of 1 per cent in the quantity of labor would, other things being equal, normally tend to be followed by a decrease of ¼ per cent in the rate of wages.”
    [He uses a production function P=1.01\,\,{{L}^{{\scriptstyle{}^{3}\!\!\diagup\!\!{}_{4}\;}}}{{C}^{{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{4}\;}}} ]
  5. Discuss this quotation from Broster: “Secondly, the chief concern of the railways is the maximization not of gross but of net revenue the maximum values of which are not the simultaneous product of the same level of fares. As is well known, the fare that attracts the former is that which corresponds to unit elasticity. It is perhaps not so well known—especially amongst the managers of sales departments—that except where the total cost remains constant for different rates of output of services, the fare that attracts the maximum net revenue is necessarily higher.”
  6. Discuss this quotation from Hicks: “The elasticity of substitution of labor for capital is the same as the elasticity of substitution of capital for labor.”

 

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library. Lloyd Appleton Metzler Papers. Box 7. [Harvard University], Division of History, Government and Economics. Division Examinations for the Degree of A.B., 1938-39.