Month: July 2015

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Chicago Courses Economists Exam Questions

Chicago. Econ 332. Business Cycle Theory (Lange). Final Exam.1938

 

 

In the previous post, we encountered Martin Bronfenbrenner who was the first choice on a short-list for a position to be filled at Columbia College. In his papers archived at the Duke University Economists’ Papers Project we find a mimeographed copy of the exam for Business Cycle Theory, Economics 332 dated December 21, 1938.  Since Bronfenbrenner was a graduate student at the University of Chicago then and the course number and title exactly coincide with those of the course offered by Oskar Lange in the Autumn Quarter 1938 that ended precisely on December 21, we can confidently match the exam below to Lange’s Business Cycle Theory course.

 

From The University of Chicago, Announcements,Vol. XXXVIII,   No. 7. The College and the Divisions for the Sessions of 1938-39. (p. 325):

E. FINANCE AND FINANCIAL ADMINISTRATION
[…]

332. Business Cycle Theory.–Historical and systematic analysis of business cycle theory. The main types of explanation. Equilibrium theory and analysis of economic processes. The role of time in the analysis of economic processes. The significance of anticipations. Theoretical and observed fluctuations. The factors which determine the general level of output and employment. The fluctuations of investment and of employment. The role of technical progress. Business-cycle policy. Prerequisite: Economics 211, 301, and 330, or their equivalents. Autumn, 1:30, LANGE.

[Highlighted text was not included in the course description from the 1942 Announcements]

________________________________

December 21, 1938

ECONOMICS 332

Business Cycle Theory

  1. State Say’s law and explain under what monetary conditions it does or does not hold good.
  2. (1) What definition of saving makes saving always equal to investment?
    (2) Indicate two definitions of saving such that saving may differ from investment and explain the meaning of this difference in each case.
    (3) Give two possible meanings of the term ‘hoarding.’
  3. Explain briefly Mr. Keynes’ doctrine concerning:
    (1) the effects on employment of a general and uniform change in money wages
    (2) the effects on total employment of relative changes in money wage rates
  4. Is there any theoretical justification for dividing the business cycle into four phases? Discuss the problem on hand of any theory of the business cycle you like to choose.

 

Source: Duke University, Rubenstein Rare Book & Manuscript Library, Martin Bronfennbrenner Papers, 1939-1995, Box 24, c.1, Folder “Exams. Macro-econ cycles & fiscal policy 1951-76. 1 of 3”.

Image source: Wikipedia/commons.

 

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Columbia Courses Economists Harvard Transcript

Columbia. Search Committee Report. 1950

This report is fascinating for a couple of reasons. The search committee understood its task to identify “the names of the most promising young economists, wherever trained and wherever located” from which a short list of three names for the replacement of Louis M. Hacker in Columbia College was selected. Organizationally, Columbia College is where undergraduate economics has been taught so that teaching excellence, including participation in Columbia College’s legendary Contemporary Civilization course sequence, was being sought as well as was potential for significant scholarship. Appendix C provides important information on James Tobin’s graduate economics education. In a later posting, I’ll provide information on others in the long-list of seventeen economists identified by the search committee.

___________________

January 9, 1950

 

Professor James W. Angell, Chairman
Department of Economics
Columbia University

Dear Mr. Chairman:

The Committee appointed by you to canvass possible candidates for the post in Columbia College that is made available by the designation of Professor Louis M. Hacker as Director of the School of General Studies submits herewith its report.

As originally constituted, this committee was made up of Professors Taylor, Barger, Hart and Haig (chairman). At an early stage the membership was expanded to include Professor Stigler and from the beginning the committee had the advantage of the constant assistance of the chairman of the department.

In accordance with the suggestions made at the budget meeting in November, the committee has conducted a broad inquiry, designed to raise for consideration the names of the most promising young economists, wherever trained and wherever located. In addition to the men known personally to the members of the committee, suggestions were solicited from the authorities at other institutions, including Harvard, Chicago, California and Leland Stanford. By mid December, scrutiny of the records and publications by the committee to the following seventeen:

 

Name Suggested by
Alchian, Armen A. Haley
Bronfenbrenner, Martin Friedman
Brownlee, O. H. Friedman
Christ, Carl L. Angell
Dewey, D. J. Friedman
Du[e]senberry, [James] Stigler
Goodwin, Richard M. Burbank
Harberger, J. H. Friedman
Ho[s]elitz, Bert Friedman
Lewis, H. Gregg Hart
Machlup, Fritz Stigler
Nicholls, William H. Stigler
Nutter, J. W. Friedman
Pancoast, Omar Taylor
Schelling, Thomas Burbank
Tobin, James Burbank
Vandermeulen, D. C. Ellis

[p. 2]

The meeting of the American Economic Association in New York during the Christmas holidays offered an opportunity to meet many of the men on the above list and to make inquiries regarding them. As a consequence, it has been possible for your committee to make rapid progress with its appraisals. Although the committee is continuing to gather information and data, it is prepared at this time to make a series of definite recommendations, with a high degree of confidence that these recommendations are not likely to be greatly disturbed by its further inquiries.

It is the unanimous opinion of the members of your committee that the most eligible and promising candidate on our list is Martin Bronfenbrenner, associate professor of economics at the University of Wisconsin, at present on leave for special service in Tokyo.

Should Bronfenbrenner prove to be unavailable the committee urges consideration of D. J. Dewey, at present holding a special fellowship at the University of Chicago, on leave from his teaching post at Iowa. As a third name, the committee suggests James Tobin, at present studying at Cambridge, England, on a special fellowship from Harvard.

Detailed information regarding the records of these three men will be found in appendices to this report.

Bronfenbrenner, the first choice of the committee, is 35 years old. He received his undergraduate degree from Washington University at the age of 20 and his Ph.D. from Chicago at 25. During his war service, he acquired a good command of the Japanese language. He taught at Roosevelt College, Chicago, before going to Wisconsin and undergraduate reports of his teaching are as enthusiastic as those of the authorities at Chicago. He happens to be personally well known to two of the members of your committee (Hart and Stigler) and to at last two other member of the department (Shoup and Vickrey), all four of whom commend him in high terms.

The following statement from Hart, dated December 6, 1929, was prepared after a conference with Friedman of Chicago:

“Bronfenbrenner is undoubtedly one of the really powerful original thinkers in the age group between thirty and thirty-five. He has always very much enjoyed teaching; my impression is that his effectiveness has been with the upper half of the student body at Roosevelt College and at Wisconsin. He is primarily a theorist but has a wide range of interest and a great deal of adaptability so it would not be much of a problem to fit him in somewhere [p. 3] in terms of specialization. He would do a good deal to keep professional discussion stirring in the University. My impression is that he tends to be underrated by the market, and that a chance at Columbia College might well be his best opportunity for some time ahead. The difficulty is, of course, that there is no chance of arranging an interview; though Shoup and Vickrey, of course, both saw him last summer.”

In a letter dated December 15, Shoup wrote as follows:

“I have a high regard for Martin Bronfenbrenner’s intellectual capacities, and I think he would fit in well in the Columbia scene. He has an excellent mind and a great intellectual independence. In his writings he sometimes tends to sharp, almost extreme statements, but in my opinion, they almost always have a solid foundation, and in conversation he is always ready to explore all sides of the question. When we had to select someone to take over the tax program in Japan, after the report had been formulated, and oversee the implementation of the program by the Japanese government, it was upon my recommendation that Bronfenbrenner was selected. He arrived in Japan in the middle of August and his work there since that time has confirmed me in my expectations that he would be an excellent selection for the job, even though he did not have very much technical background in taxation. I rank him as one of the most promising economists in his age group in this country, and I should not be surprised if he made one or more major contributions of permanent value in the coming years.

“He has gone to Japan on a two year appointment, after having obtained a two year leave of absence from the University of Wisconsin. My understanding is that on such an appointment he could come back to the United States at the end of one year, provided he paid his own passage back. It might be possible that even this requirement would be waived, but I have no specific grounds for thinking so. I believe the major part of his work with respect to implementing the tax program will have been completed by next September. If the committee finds itself definitely interested in the possibility of Bronfenbrenner’s coming to Columbia, I should not let the two year appointment stand in the way of making inquiries.”

The breadth and rang of his interests recommend Bronfenbrenner as a person who would probably be highly [p.4] valuable in the general course in contemporary civilization and the quality of his written work suggests high promise as a productive scholar in one or more specialized fields.

Your committee considers that the appropriate rank would be that of associate professor.

Respectfully submitted,

[signed]

Robert M. Haig

 

______________________________

Appendix A – Martin Bronfenbrenner

The following data regarding Bronfenbrenner are taken chiefly from the 1948 Directory of the American Economic Assoication:

Born: 1914

Education and Degrees:

A.B. Washington University, 1934
Ph.D. University of Chicago 1939
1940-42, George Washington School of Law

Fields: Theory, mathematical economics, statistical methods, econometrics

Doctoral dissertation: Monetary theory and general equilibrium

Publications:

“Consumption function controversy”, Southern Economic Journal, January, 1948
“Price control under imperfect competition”, American Economic Review, March, 1947
“Dilemma of Liberal Economics,” Journal of Political Economy, August, 1946

Additional publications:

“Post-War Political Economy: The President’s Reports”, Journal of Political Economy, October, 1948
Various book reviews including one on W. I. King’s The Keys to Prosperity, Journal of Political Economy, December, 1948, and A. H. Hansen’s Monetary Theory and Fiscal Policy, Annals

Additions to list of publications circulated, January 9, 1950

“The Economics of Collective Bargaining”, Quarterly Journal of Economics, August, 1939.
(with Paul Douglas) “Cross-Section Studies in the Cobb-Douglas Function”, Journal of Political Economy, 1939.
“Applications of the Discontinuous Oligopoly Demand Curve”, Journal of Political Economy, 1940.
“Diminishing Returns in Federal Taxation” Journal of Political Economy, 1942.
“The Role of Money in Equilibrium Capital Theory”, Econometrica (1943).

______________________________

Appendix B – D. J. Dewey

On leave from Iowa.

In 1948 studied at Cambridge, England.
1949-50, at Chicago on special fellowship.

Bibliography:

Notes on the Analysis of Socialism as a Vocational Problem, Manchester School, September, 1948.
Occupational Choice in a Collectivist Economy, Journal of Political Economy, December, 1948.

Friedman and Schultz are highly enthusiastic.

Statement by Hart, dated December 6, 1949:

“Friedman regards Dewey as first rate and points to an article on ‘Proposal for Allocating the Labor Force in a Planned Economy’ (Journal of Political Economy, as far as I remember in July 1949) for which the J.P.E. gave a prize as the best article of the year. I read the article, rather too quickly, a few weeks ago and it is definitely an imaginative and powerful piece of work. How the conclusions would look after a thorough-going seminar discussion, I am not clear; but the layout of questions is fascinating.”

______________________________

Appendix [C] – James Tobin

Statement by Burbank of Harvard, dated December 14, 1949:

“We have known Tobin a good many years. He came to us as a National Scholar, completed his work for the A.B. before the war and had advanced his graduate work very well before he went into the service. He received his Ph.D. in 1947. Since 1947 he has been a Junior Fellow. He was a teaching fellow from 1945 to 1947. He is now in Cambridge, England, and will, I believe, begin his professional work by next fall. Since Tobin has been exposed to Harvard for a very long time I believe that he feels that for his own intellectual good he should go elsewhere. I doubt if we could make a stronger recommendation than Tobin nor one in which there will be greater unanimity of opinion. Certainly he is one of the top men we have had here in the last dozen years. He is now intellectually mature. He should become one of the handful of really outstanding scholars of his generation. His interests are mainly in the area of money but he is also interested in theory and is competent to teach at any level.”

Data supplied by Harvard:

Address:    Department of Applied Economics, Cambridge University, England

Married:   Yes, one child

Born:          1918, U.S.

Degrees:

A. B. Harvard, 1939 (Summa cum laude)
A.M. Harvard, 1940
Ph.D. Harvard, 1947

Fields of Study: Theory, Ec. History, Money and Banking, Political Theory: write-off, Statistics

Special Field: Business Cycles

Thesis Topic: A Theoretical and Statistical Analysis of Consumer Saving

Experience:

1942-45 U.S. Navy
1945-47 Teaching Fellow, Harvard University
1947- Junior Fellow, Society of Fellows

[p. 2 of Appendix C]

Courses:           1939-40

Ec. 21a (Stat.)                  A
Ec. 121b (Adv. St.)          A
Ec. 133 (Ec. Hist)            A
Ec. 147a (M&B Sem)      A
Ec. 145b (Cycles)             A
Ec. 113b (Hist. Ec.)       Exc.
Gov. 121a (Pol.Th.)         A

1940-1941

Ec. 121a (Stat.)                A
Ec. 164 (Ind. Org.)          A
Ec. 20 (Thesis)                A
Ec. 118b (App. St.)          A
Math 21                             A
Ec. 104b (Math Ec.)       A

1946-47 Library and Guidance

Generals:       Passed May 22, 1940 with grade of Good Plus
Specials:         Passed May 9, 1947 with grade of Excellent.

 

Data from 1948 Directory of American Economic Association:

Harvard University, Junior Fellow

Born:                1918

Degrees:           A. B., Harvard, 1939; Ph.D., Harvard, 1947j

Fields: Business fluctuations, econometrics, economic theory, and mathematical economics

Dissertation: A theoretical and statistical analysis of consumer saving.

Publications:

“Note on Money Wage Problem”, Quarterly Journal of Economics, 1941.
“Money Wage Rates and Employment”, in New Economics (Knopf, 1947).
“Liquidity Preference and monetary Policy”, Review of Economics and Statistics, 1947.
[pencil addition] Article in Harris (ed.), The New Economics, 1947.

______________________________

Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”

Image Source: The beyondbrics blog of the Financial Times.

Categories
Columbia Courses Economists

Columbia. Course Descriptions. Hotelling. 1931-1945

Class rolls from Hotelling’s courses on mathematical economics he taught at Columbia have been posted, as have course outlines and a final exam from the course as taught at the University of North Carolina in 1946 and 1950.

_________________________

[1931-32]

Economics 311-312—Statistical inference. 3 points each session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.

Summarizing and interpretation of data; probability, mathematical and philosophical; the normal law of error; probable errors; student’s distribution and the work of R. A. Fisher; least squares; fitting trend lines and other empirical curves; their reliability; accuracy of forecasts; tests of stability, homogeneity, and goodness of fit; analysis of variance; simple, partial and multiple correlation coefficients and their interpretation in terms of probability; periodogram analysis.

Prerequisite: Calculus. A knowledge of determinants is desirable.

 

Economics 313-314—Mathematical economics. 3 points each session. Professor H. Hotelling.
M. and W. at 4:10. 302 Fayerweather.

Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.

Prerequisite: Calculus.

 

[1932-33]

Economics 311—Statistical inference. 3 points Winter Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.

Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; Student’s distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.

Prerequisite: Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) must be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Economics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.

Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.

Economics 312—Modern statistical theory. 3 points Spring Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.

Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.

Prerequisites: Economics 311 and Mathematics 57 and 101.

 Economics 313-314—Mathematical economics. 3 points each session. Professor H. Hotelling.
M. and W. at 4:10. 302 Fayerweather.

Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.

Prerequisite: Calculus. Mathematics 57 will also be found helpful, though it is not a required prerequisite.

 

[1933-34]

[Starting this year the two courses in Statistics were moved from “Research Courses” to “General Courses” as reflected in the course numbering. Note the label “Statistics” instead of “Economics” before the course numbers]

Statistics 111—Statistical inference. 3 points Winter Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.

Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; Student’s distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.

Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) should be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Statistics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.

Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.

Statistics 112—Statistical inference. 3 points Spring Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.

Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.

Prerequisites: Economics 111 and Mathematics 57 and 101 or equivalent knowledge.

Economics 117-118—Mathematical economics. 3 points each session. Professor H. Hotelling. [Starting this year Mathematical Economics was moved from “Research Courses” to “General Courses” as reflected in the course numbering.]
M. and W. at 4:10. 418 Business.

Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.

Prerequisite: Calculus. Mathematics 57 will also be found helpful, though it is not a required prerequisite. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.

 

[1934-35]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.

Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; student’s [sic] distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.

Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) should be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Statistics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.

Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.

Statistics 112—Statistical inference. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.

Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.

Prerequisites: Economics [sic, Statistics] 111 and Mathematics 57 and 101 or equivalent knowledge.

Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
[According to Bulletin 1935-36 this course was given in 1934-1935 but not given in 1935-1936]

Economics 117-118—Mathematical economics. 3 points each session. Professor Hotelling.
M. and W. at 4:10. 418 Business.

The fundamentals of economics as a set of problems in maxima and minima. The maximizing of utility or of profits by individuals and the consequent equations of general equilibrium; the nature and interrelations of utility, curves and surfaces of indifference, demand and supply functions, consumers’ surplus, and welfare. Monopoly and various forms of competition. The extent to which selfish activities of individuals promote the general welfare; contrasts and resemblances of a planned society with the outcome of competition. Interrelation of prices. Taxation. Dynamical economics: cycles, lagging effects, and exhaustible resources.

The theory of maxima and minima of functions of n variables, with and without restraining conditions; the elements of the calculus of variations; tensors. The effects of variation of parameters on maximizing conditions are applied to discover consequences of taxation and other interferences.

A thorough knowledge of calculus, with something of differential equations, is an essential prerequisite. Mathematics 57 (Higher algebra; M., W., and F. at 11) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.

 

[1935-36]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 4:10 611 Business.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.

Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.

 

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Diverse applications, both to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, Mathematics 57, and Mathematics 101 or equivalent knowledge.

Statistics 114 [new course]—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 4:10. 611 Business.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory.

Prerequisites: Statistics 111, Mathematics 57 and Mathematics 101.

[Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Given in 1934-1935; not to be given in 1935-1936]

Economics 117 [Course reduced to a single semester]—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 507 Business.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Theory of interest, depreciation, exhaustible resources. Contrasts and resemblances of a planned society with the outcome of competition. Dynamical economics: cycles and lagging effects.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions. Elements of the calculus of variations.

Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.

[1936-37]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 4:10 611 Business.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.

Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Diverse applications, both to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, Mathematics 57, and Mathematics 101 or equivalent knowledge.

Statistics 114 [new course]—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 4:10. 611 Business.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory.

Prerequisites: Statistics 111, Mathematics 57 and Mathematics 101.

[Statistics 302—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Not listed in Bulletin 1936-1937] 

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. M. in 401 Fayerweather and W. in 412 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.

 

[1937-38]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 5:10 228 Pupin.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.

Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.

[Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Not given in 1937-38]

[Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
Not given in 1937-38]

Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Hours to be arranged.

Prerequisites: Statistics 111, 112, and 114, or similar knowledge of statistical theory.

[Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.

Not given in 1937-38]

 

[1938-39]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 5:10 412 Fayerweather.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.

Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 58, and Mathematics 107.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 11. 412 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.

Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 5:10. 412 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory. The efficient design of investigations.

Prerequisites: Same as for Statistics 112.

[Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Not given in 1938—1939]

Prerequisites: Statistics 111, 112, and 114.

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 11. M. in 412 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.

 

[1939-40]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling and Dr. Wald.
M. and W. at 5:10 412 Fayerweather.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.

Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.

Attention is called also to Mathematics 108 (calculus of finite differences, given by Professor Koopman, M. and W., 1:45-3). Graduate credit in economics will be allowed for Mathematics 58, 107, and 108.

Numerical methods, including the use of punched-card equipment, may be learned in Astronomy 110.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling and Dr. Wald.
M. and W. at 5:10. 412 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.

Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling and Dr. Wald.
M. and W. at 11. 224 Pupin.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory. The efficient design of investigations.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.

Prerequisites: Statistics 111, 112, and 114.

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling and Dr. Wald.
M. and W. at 11. M. 228 Pupin.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.

 

[1940-41]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:30—6:20. 410 Fayerweather.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.

Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 58 and 107.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.

Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W., 5:30—6:20. 410 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.

Prerequisites: Statistics 111, 112, and 114.

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 401 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.

 

[1941-42]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.

Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.

Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 57 (higher algebra) is recommended.

Graduate credit in economics will be allowed for Mathematics 57 and 107.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.

The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.

Statistics 114—Correlation and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.

Prerequisites: Statistics 111, 112, and 114.

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 107.

 

[1942-43]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.

The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.

A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Mathematics 167 is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.

Graduate credit in economics will be allowed for Mathematics 107 and 167. For these courses see the Announcement of the Division of Mathematical and Physical Sciences.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.

Statistics 114—Correlation and the χ2 test. 3 points Spring Session. Professor Hotelling.
Tu. and Th., 5:40—6:30. 410 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
W. at 8 p.m. 304 Fayerweather.

Prerequisites: Statistics 111, 112, and 114. 

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 167 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 167 and Mathematics 107.

 

[1943-44]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 305 Schermerhorn.

The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.

A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Higher algebra is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.

Graduate credit in economics will be allowed for Mathematics 107 and 57. For these courses see the Announcement of the Division of Mathematical and Physical Sciences.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 410 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.

Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
Hours to be arranged.

Prerequisites: Statistics 111, 112, and 114.

Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.

The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.

The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.

Prerequisite: A thorough knowledge of calculus. Mathematics 167 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 167 and Mathematics 107.

 

[1944-45]

Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 305 Schermerhorn.

The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.

A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Higher algebra is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.

Graduate credit in economics is allowed for these mathematics courses, for which see the Announcement of the Division of Mathematical and Physical Sciences.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th at 10. 410 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.

Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 410 Fayerweather.

The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. Contingency tables.

The distribution of the correlation coefficient is derived and is used to illustrate various logical and mathematical questions of more general application.

Prerequisites: Same as for Statistics 112.

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
Hours to be arranged.

Prerequisites: Statistics 111, 112, and 114.

 [Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Not given in 1944-1945]

 

[1945-46]

Statistics 111a and 111b—Probability and statistical inference. 3 or 6 points Winter Session. Professor Hotelling.

Tu. and Th., at 5:40—6:30 and 7:30—8:20. 305 Schermerhorn.

The fundamental prerequisite to all other courses in mathematical statistics. Statistics 111a (Probability) covers the first half of the session and Statistics 111b (Statistical inference) the second half. Students may register for the first half alone, or, if they have completed a course in mathematical probability, for the second half alone. Those intending to study both parts should register for both at the beginning of the session. Registration for Statistics 111b should be completed not later than November 15.

The classical mathematical theory of probability is developed in the first half, starting from a critical treatment of the basic concepts and including permutations and combinations, the binomial, Poisson and normal distribution, the Law of Great Numbers, the principal limit theorems, geometrical probability, and the characteristic function. The second half introduces the use of observations to estimate unknown quantities and to test hypotheses, and deals with criteria of valid, efficient, and exact estimation, with illustrations drawn from physical, biological, and social sciences. The method of maximum likelihood is considered. The Student distribution and the variance distribution are derived and applied to various situations. Moments, cumulants, and other quantities are considered in their two meanings as parameters of a “population,” or probability distribution, and as estimates of parameters based on a “sample” of observations.

A thorough knowledge of calculus is an essential prerequisite. Students are advised to study Mathematics 167 simultaneously to obtain a knowledge of matrix algebra for use in more advanced statistics courses and in mathematical economics.

Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Wald. [Note change in instructor.]
Tu. and Th at 10. 410 Fayerweather.

The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.

Prerequisites: Statistics 111b, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111a and 111b.

[Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Not given in 1945-1946]

Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Wald.  [Note change in instructor.]
Tu., 8-10 p.m. 618 Business.

Prerequisites: Statistics 111a and b, 112, and 114. 

[Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Not given in 1945-1946]

___________________

 

Source: Columbia University. Bulletin of Information. History, Economics, Public Law, and Social Science [1931-32—1940-41]; History, Economics, Public Law, and Sociology [1941-42—1945-46]. Courses offered by the Faculty of Political Science.

Image source: From a photo of the Institute of Statistics leadership around 1946: Gertrude Cox, Director, William Cochran, Associate Director-Raleigh and Harold Hotelling, Associate Director-Chapel Hill. North Carolina State University.

Categories
Columbia Economists

Columbia Economics. Mathematical Economics. Hotelling. Class Rolls 1931-1944

Hotelling’s students included the communist and later Soviet agent Victor Perlo (1932-33) and three Nobel prize winners in economics, Milton Friedman (1933-34), William Vickrey (Winter session 1935-36) and Kenneth Arrow (Winter session 1940-41).  Friedman’s and Arrow’s student notes for this course with Hotelling can be found at the Hoover Archives and the Duke Economist Papers Project, respectively. 

Course outlines and a final examination for Hotelling’s course as taught at the University of North Carolina in 1946 and 1950 has been posted. Here is a link to the posting of a list of statistics and economics courses taught at Columbia by Harold Hotelling.

____________________________

Econ 312. Mathematical Economics

 Winter Session, 1931-32
Benitz, Paul A.
Kelly, Thomas H.
Metzger, Henry W.
Pabst, William R., Jr.
Wu, Kan
Columbia College Madow, William
School of Business Otto, Erich A.
School of Business Stein, Arthur
Econ 314. Mathematical Economics Spring Session, 1931-32
Benitz, Paul A.
Duncan, Acheson Johnston
Kelly, Thomas H.
Pabst, William R. (Jr)
Metzger, Henry W.
Econ 313. Mathematical Economics Winter session, 1932-33
Lawson, Alfred
Perlo, Victor
Preinreich, Gabriel A.D.
Weyl, Nathaniel
Econ 314. Mathematical Economics  Spring Session, 1932-33
Perlo, Victor
Preinreich, Gabriel A. D.
Weyl, Nathaniel
Econ 117. Mathematical Economics Winter session, 1933-34
Dodwell, David W.
Edmondson, Susanna P.
Friedman, Milton
Goldberg, Henry
Madow, William G.
Vass, Laurence C.
School of Business Osborne, Ernest L.
Econ 118. Mathematical Economics Spring Session, 1933-34
Edmondson, Susanne P.
Friedman, Milton
Goldberg, Henry
Vass, Laurence C.
Econ 117. Mathematical Economics Winter Session, 1934-35
Bonis, Austin J.
Frankel, Lester R.
Wright, Charles A.
Econ 118. Mathematical Economics Spring Session, 1934-35
  Bonis, Austin J.
Frankel, Lester R.
Machol, Richard M.
Richards, Margaret H.
Romig, Harry G.
Solomons, Leonard M.
Wright, Charles A.
Econ 117. Mathematical Economics Winter Session, 1935-36
Bennett, Rollin F.
Fabricant, Solomon
Hilfer, Irma
Jacobson, Katharine
Norton, John D.
Vickrey, William
Wallis, W. Allen
Econ 117. Mathematical Economics Class rolls not found for 1936-37
Econ 117. Mathematical Economics Not offered 1937-38
Econ 117. Mathematical Economics Winter Session, 1938-39
Dejongh, Theunis W
Durand, David
Friedman, Irma D.
Geisler, Murray A.
Gould, Jacob M.
King, Frederick G.
Schwartz, Seymour
Shulman, Harry
Columbia College Klarman, Herbert
Teachers College Recht, Leon Samuel
Econ 117. Mathematical Economics Winter Session, 1939-40
Bennett, Blair M.
Nassimbene, Raymond
Pascale, Henry
Columbia College Schwartz, Harry
Econ 117. Mathematical Economics Winter Session, 1940-41
Arrow, Kenneth J.
Berger, Richard
Cohen, Leo
Divatia, Makarand V.
Fischer, Harry S.
Haines, Harold
Konijn, Hendrik S.
Peiser, Donald E.
School of Business Ballentine, George A.
Econ 117. Mathematical Economics Winter Session, 1941-42
Diamond, Harold S.
Peach, Paul
Ravitsky, Inda
Reder, Melvin W.
Sievers, Allen M.
School of Business Cooper, William W.
School of Business Morrison, Lachlan
Econ 117. Mathematical Economics Winter Session, 1942-43
Boyd, Elizabeth N.
D’Errico, John E.
Simpson, Elizabeth T.
Simpson, William B.
Columbia College Tenenbaum, Warren S.
School of Business Lopata, Simon
Econ 117. Mathematical Economics Winter Session, 1943-44
Hsieh, Kia
Lindsey, Fred D.
Owlett, Ann M.
Straus, Everett M.
Ullman, Joseph L.
School of Business

Varon, Frank R.

Source: Assembled from the student registration cards. Columbia University. Rare Book & Manuscript Library. Hotelling Papers, Box 48, Folder Mathematical Economics (1).

Categories
Columbia Cornell Economists Pennsylvania Yale

Portrait of Eight Economists. University Extension Summer Meeting. 1894

This set of pictures was found in Box 2, Folder “Photographs” of the Franklin Henry Giddings papers, 1890-1931, Columbia University, Rare Book & Manuscript Library. Judging from the college/university affiliations given (about a two year window) and the fact that the Seventh Annual Meeting of the American Economic Association was held with Columbia College, New York City, December 26-29, 1894, my first guess was that this was related to the AEA event and put together by the local organizers.

However we can be certain that this handsome collection of portraits was published instead as a supplement to the University Extension Bulletin. Exactly these eight economists are the “corps of lecturers” for the University Extension Summer Meeting held July 2-28, 1894 at the University of Pennsylvania as described in The University Extension Bulletin, Vol. I, No. 8 (May 10, 1894). Further it is announced: “We present our readers also with a supplement with portraits of the lecturers in the Economics Department.” Here at haithitrust.org is that supplement.

 

Probably this collection of portraits is related to the 7th Annual AEA Meeting at Columbia Dec 26-29, 1894.

Categories
Chicago Courses

Chicago Economics. Reading Assignments, Economic Theory (Econ 301). Viner, Fall 1932

In Milton Friedman’s papers at the Hoover Institution Archives there is a one page handwritten list of reading assignments for Jacob Viner’s Economics 301 (Economic Theory) in Box 5, Folder 12 and a one page typed list of reading assignments for the course, Box 5 Folder 13, that is nearly identical (with only two discrepancies) to the reading list “reproduced exactly from the document that the editors have in their possession” in the appendix to Jacob Viner: Lectures in Economics 301. Douglas A. Irwin and Steven G. Medema, editors. Transaction Publishers, 2013. The lecture notes taken by Marshall D. Ketchum that have been published by Irwin and Medema were taken in the Summer Quarter 1930, two years before Milton Friedman took the course in the Fall Quarter 1932. Everything below in brackets are my additions/annotations.

______________________

[Handwritten notes by Milton Friedman]

Assignments given by Viner in 301, 1932

Marshall        Bk III  ch 3 + 4; Bk V ch 1 + 2

[Alfred Marshall, Principles of Economics (London: Macmillan and Co. 8th ed. 1920).
Book III: On wants and their satisfaction.
Chapter 3: Gradations of consumers’ demand;
Chapter 4: The elasticity of wants.
Book V: General relations of demand, supply and value.
Chapter 1: Introductory. On markets;
Chapter 2: Temporary equilibrium of demand and supply.]

Schultz           Meaning of st[atistical] de[mand] cur[ves] pp 1-10; 25-41.

[Henry Schultz. Statistical Laws of Demand and Supply with Special Application to Sugar. Chicago: University of Chicago Press. 1928. 118 pages]

Mars[hall]      Bk V ch 3, 4, 5, 12; App H

[Book V: General relations of demand, supply and value.
Chapter 3: Equilibrium of normal demand and supply;
Chapter 4: The investment and distribution of resources;
Chapter 5: Equilibrium of normal demand and supply, cont., with reference to long and short periods;
Chapter 12: Equilibrium of normal demand and supply, cont., with reference to the law of increasing returns.
Appendix H: Limitations of the use of statical assumptions in regard to increasing return.]

Viner             Cost Curves […]

[…and Supply Curves, Zeitschrift für Nationalökonomie. Bd. 3, H. 1 (1931), pp. 23-46]

Cunynghame “Geometrical Political Economy”, ch. 3

[Henry H. Cunynghame. A Geometrical Political Economy: Being an Elementary Treatise on the Method of Explaining Some of the Theories of Pure Economic Science by Means of Diagrams, Oxford at the Clarendon Press. 1904.
Chapter 3: Demand curve.]

Smart, Introduction to theory of value     pp. 64-83

[Smart, William (1891). An Introduction to the Theory of Value on the Lines of Menger, Wieser, and Böhm-Bawerk. London and New York, Macmillan and Co. 1891.
Chapter 12: Cost of production;
Chapter 13: From marginal products to cost of production;
Chapter 14: From cost of production to product;
Conclusion.]

Böhm-Bawerk:

“Ultimate standard of value”, Annals of Am[erican] Academy Sept. [sic] 1894

[Eugen von Böhm-Bawerk. The ultimate standard of value. American Academy of Political and Social Science, Philadelphia. Publications, no. 128. June, 1894, 60 p.]

“One word more on ult. st. of v. [ultimate standard of value]   E.J. Dec. 1894

[Eugen von Böhm-Bawerk. One word more on the ultimate standard of value. Economic Journal, Vol. 4, No. 16 (Dec., 1894), pp. 719-725.]

Marshall        Bk V, ch 6;  Bk V, ch 14

[Book V, ch 6: Joint and composite demand. Joint and composite supply.
Book V, ch 14: The theory of monopolies.]

Viner              JPE. 1925 pp 107-111 (objective test of comp.[etitive] price appl[ied] to cem[ent] ind[ustry])

[Jacob Viner, Objective tests of competitive price applied to the cement industry. Journal of Political Economy, Vol. 33, No. 1 (Feb., 1925), pp. 107-111.]

J.S.Mill “Outline of Pol. Economy” Bk II, Ch 11, sec 1; Bk I, ch VI, sec 1

[Note: Outline of Political Economy is the title of Nassau Senior’s book.
John Stuart Mill, The Collected Works of John Stuart Mill, Volume II – The Principles of Political Economy with Some of Their Applications to Social Philosophy (Books I-II), ed. John M. Robson, introduction by V.W. Bladen (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1965).
Book II, ch XI, sec. 1:  Distribution. Of wages.
Book I, ch VI, sec. 1: Production. On circulating and fixed capital.]

Henry George, “Progress + Poverty”         Bk I, ch 1,3,4

[Henry George, Progress and Poverty: An Inquiry into the Cause of Industrial Depressions and of Increase of Want with Increase of Wealth, The Remedy (Garden City, NY: Doubleday, Page, & Co. 1912).
Book I: Wages and Capital.
Chapter 1: The current doctrine of wages–its insufficiency;
Chapter 3: Wages not drawn from capital, but produced by labor;
Chapter 4: The maintenance of laborers not drawn from capital.]

F.W. Taussig, Principles, vol II, ch 39, 51

[Frank W. Taussig, Principles of Economics. 2nd revised edition. 2 vols. (New York: Macmillan). 1915. Note: a later 3rd revised edition from 1921 has a chapter 51 “Great fortunes” that does not appear as good a fit to this course’s content, so I conclude the reference is to the second edition.
Chapter 39: Interest, cont. The equilibrium of demand and supply;
Chapter 51: General wages.]

J.B. Clark “Dist[ribution] of Wealth”, ch 1, 7, 8, + Preface

 [John Bates Clark, The Distribution of Wealth: A Theory of Wages, Interest and Profits (New York: Macmillan). 1899.
Chapter I: Issues That depend on Distribution;
Chapter VII: Wages in a Static State, the Specific Product of Labor;
Chapter VIII: How the Specific Product of Labor may be Distinguished.]

F.A. Walker, Political Economy P[reface] + IV, ch 4,5,8 + V [sic, should be VI], sec 5

[Francis Amasa Walker, Political Economy (London: Macmillan) 3rd revised and enlarged edition. 1892.
Part IV: Distribution.
Chapter 4: Profits;
Chapter 5: Wages;
Chapter 8: The reaction of distribution upon production.
Part VI: Some applications of economic principles.
Section V: The doctrine of the wage-fund.]

A. Smith Bk I, ch 10

[Adam Smith An Inquiry into the Naature and Causes of the Wealth of Nations, Edwin Cannan, 3d. London: Methuen & Co., Ltd. 5th edition, 1904.
Book I, Chapter X: Of wages and profit in the different employments of labour and stock.]

J.S. Mill           Bk II, ch 14

[Book II, ch 14: Distribution. Of the differences of wages in different employments.]

Cairnes “Polit. Econ”, P[reface] + I, ch 3 [art.] 4,5

[J.E. Cairnes. Some Leading Principles of Political Economy Newly Expounded. New York: Harper & Brothers, Publishers. 1874.
Part I: Value.
Chapter 3: Normal value]

Taussig          Principles, ch 47

[Chapter 47: Differences of wages. Social stratification.]

J. B. Clark Ch 9, 13

[Chapter IX: Capital and Capital-Goods Contrasted;
Chapter XIII: The Products of Labor and Capital, as Measured by the Formula of Rent]

Böhm Bawerk           Bk 2, ch 1-5; Bk 5, ch 1-4; Bk 6, ch 1,2,4,5,6; Bk 7, ch 1,2

[Book II: Capital as instrument of production.
Chapter 1: Introductory;
Chapter 2: Capitalist production;
Chapter 3: Historical development of the conception;
Chapter 4: The true conception of capital;
Chapter 5: The competing conceptions of capital.
Book V: Present and future.
Chapter 1: Present and future in economic life;
Chapter 2: Differences in want and provision for want;
Chapter 3: Unerestimate of the future;
Chapter 4: The technical superiority of present goods.
Book VI: The source of interest.
Chapter 1:  The loan and loan interest
Chapter 2: The profit of capitalist undertaking. Principles of explanation.
Chapter 4: The profit of capitalist undertaking. The labour market;
Chapter 5: The profit of capitalist undertaking. The general subsistence market;
Chapter 6: The profit of capitalist undertaking. The general subsistence market (continued).
Book VII: The rate of interest.
Chapter 1: The rate in isolated exchange;
Chapter 2: The rate in market transactions.]

Marshall                    Bk VI, ch IX

[Book VI: The distribution of the national income.
Chapter 9: Rent of land.]

Ogilvie                       Marshall on Rent      Econ J. 1930

[F.W. Ogilvie. Marshall on Rent. Economic Journal 40 (March) 1930: 1-24]

J.B. Clark        ch 23

[Chapter XXIII: The Relation of All Rents to Value and Thus to Group Distribution]

 Source: Hoover Institution Archives, Milton Friedman Papers Box 5, Folder 12 (Student years)

______________________

[typed list of reading assignments]

Assignments in Viner’s Economics 301
(In order of assignment)

Marshall,        Bk III, ch. 3, 4; Bk V, ch. 1, 2

Böhm-Bawerk, Positive Theory of Capital, Bk IV, ch. 4

Schultz, Meaning of Statistical Demand Curves, pp. 1-10, 25-41.

Marshall, Bk. V, ch 3, 4, 5, 12; App. H

Viner, Cost Curves [and Supply Curves, Zeitschrift für Nationalökonomie. Bd. 3, H. 1 (1931), pp. 23-46]

Cunynghame, Geometrical Political Economy, Ch. 3

Smart, Introduction to the Theory of Val., pp. 64-83

B. B. [Böhm-Bawerk], Ultim. Stand. of Val., Ann. of Am. Ac., Sept. 1894

One word More on Ult. S. of V., Econ. Jour., Dec 1894

Marshall,        Bk. V, ch. 6; Bk. V, ch. 14

Viner, Objective Tests of Comp. Pr. appl. to the Cem. Ind. JPE, ‘25

J.S. Mill, Outline of Pol Ec. [sic, Principles of Political Economy], Bk II, ch. 11, sec. 1; Bk I, ch. 6 sec. 1

Henry George, Progress and Poverty, Bk I, ch. 1, 3, 4.

F. W. Taussig, Principles, Vol II, ch 39, 51.

J. B. Clark, Distr. of Wealth, ch. 1, 7, 8, preface.

F. A. Walker, Pol. Ec., Part IV, ch. 4, 5. Part VI, Sec. 5

Adam Smith, Bk. I, ch 10

J.S. Mill, Bk II, ch. 14

Cairnes, Pol. Ec., Part I, ch. 3, arts. 4, 5.

Taussig, ch. 47

J. B. Clark, ch. 9, 13

B.B. [Böhm Bawerk], Bk II, ch 1-5; Bk V, ch 1-4; Bk. VI, ch. 1, 2,4,5,6; Bk. VII, ch. 1,2.

Marshall, Bk. VI, ch. 9

Ogilvie, Marshall on Rent, Econ. Journ., March, 1930

J. B. Clark, ch. 23

Source:  Hoover Institution Archives, Milton Friedman Papers Box 115, Folder 13 (Class Exams circa 1932-1938)

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

Categories
Chicago Columbia Economists Transcript

Milton Friedman’s Coursework in Economics, Statistics and Mathematics

Before Milton Friedman could be a teacher of economics, he was of course the student of many teachers. This list of his relevant coursework and teachers is complete. I merely add here that his transcript also shows three semesters of college French and four semesters of college German and that he entered Rutgers with advanced credits in French.

Rutgers University
University of Chicago
Columbia University
Dept. of Agriculture Graduate School

Rutgers University (1928-32)

Principles of Economics E. E. Agger 1929-30
Money and Banking E. E. Agger 1930-31
Statistical Methods Homer Jones 1930-31
Business Cycles Arthur F. Burns 1931-32
Economic Research Ivan V. Emelianoff 1931-32
Principles of Insurance Homer Jones 1931-32
College Algebra 1928-29, 1st term
Analytical Geometry 1928-29, 2nd term
Calculus 1929-30
Advanced Calculus 1930-31
Theory of Numbers 1929-30, 2nd term
Theory of Equations 1930-31, 1st term
Differential Equations 1930-31, 2nd term
Analysis 1931-32
Elliptic Integrals 1931-32, 2nd term

 

University of Chicago (1932-33, 1934-35)

Econ 301 Prices and Distribution Theory Jacob Viner Autumn Quarter 1932
Econ 302 History of Economic Thought Frank H. Knight Winter Quarter 1933
Econ 303 Modern Tendencies in Economics Jacob Viner Spring Quarter 1933
Econ 311 Correlation and Curve Fitting Henry Schultz Winter Quarter 1933
Econ 312 Statistical Graphics Henry Schultz Spring Quarter 1933
Econ 330 Graduate Study of Money and Banking Lloyd W. Mints Autumn Quarter 1932
Econ 370 International Trade and Finance Jacob Viner Winter Quarter 1933
Econ 220 Economic History of the United States, not taken for credit Chester Wright Winter Quarter 1935
Econ 220 Economic History of Europe, not taken for credit John U. Nef Autumn Quarter 1934
Labor (visited) Paul H. Douglas  1934-35
Theory of Demand (visited) Henry Schultz  1934-35
Math 306 Introduction to Higher Algebra  E. Dickson Autumn Quarter 1932
Math 341 Calculus of Variations  G. Bliss Autumn Quarter 1932
Math 324 Theory of Algebraic Numbers  A. Albert Winter Quarter 1933
Math 310 Functions of a Complex Variable (not taken for credit) L. M. Graves

 Master’s thesis: An empirical study of the relationship between railroad stock prices and railroad earnings for the period 1921-31.

 

Columbia University (1933-34)

Stat 111-12 Statistical Inference Harold Hotelling Winter/Spring semesters
Econ 117-18 Mathematical Economics Harold Hotelling Winter/Spring semesters
Econ 119 Economic History V. G. Simkhovitch Winter semester
Econ 128 Currency and Credit James W. Angell Spring semester
Econ 211-12 Business Cycles Wesley Claire Mitchell Winter/Spring semesters
Econ 315-16 Economic Theory Seminar John M. Clark, James W. Angell, and Wesley C. Mitchell Winter/Spring semesters
Social Economics (visited) J. M. Clark
Labor (visited) Leo Wolman
Theory (visited) R. W. Souter

 

Department of Agriculture Graduate School (1936-37)

Statistics 17-18 Adjustment of Observations

Source: Assembled from transcripts and course lists kept by Milton Friedman. Hoover Institution Archives, Milton Friedman Papers, Box 5, Folders 11, 13 (Student years).

Image Source: Columbia University, Columbia 250 Celebrates Columbians Ahead of Their Time.

Categories
Chicago Courses Syllabus

Chicago Economics. Math Econ (Econ 402). Henry Schultz References. 1932

 

 

Albert G. Hart was a graduate student at the University of Chicago 1931-34. Among the courses he took was that of Henry Schultz in mathematical economics. In his papers are three sets of reading lists for the course along with Hart’s handwritten notes.

Course Description Econ 402
References for Econ. 402
References for Cost Theory
References for Monopolistic Competition

The same core reading list was used in the autumn quarter of 1935. The reading list for that quarter has been transcribed in a later post, with the added attraction of having many links to the individual items on the list!

________________________________

 

  1. Mathematical Economics.—A study of economic theory from the point of view of assumptions, range of problems, methods and tools, and validity and utility of results under present conditions. Consideration is given to the problem of “circular reasoning” in price theory, to the advantages and limitations of the mathematical approach, and to the possibility of developing a “statistical complement” to pure theory. Special attention is paid to the problem of price determination and to the mathematical theory of production. Readings will be assigned on special topics in the works of Cournot, Jevons, Walras, Pareto, Marshall, Moore, and others; and the class meetings will be devoted chiefly to discussion. Opportunity for investigation of particular problems is offered the student. Prerequisite: Economics 301 [Price and Distribution Theory], a reading knowledge of French, and consent of the instructor. Registration may be made for one or more courses each quarter. Summer, Spring, SCHULTZ.

 

Source: University of Chicago. Announcements, Social Sciences for the sessions of 1931-32. Vol. XXI, January 15, 1931, no. 11, p. 26

________________________________

[Spring Quarter 1932]

REFERENCES FOR ECON. 402

Mathematical Economics
By
Henry Schultz
University of Chicago

 

Amoroso, Luigi Lezioni di Economia Matematica
Le Equazioni Differenziali della Dinamica Economica—in Giornale degli Economisti, February, 1929.
La Curva Statica di Offerta—Giornale degli Economisti, January, 1930.
Annals of the American Academy of Political & Social Science July, 1892 (Paper by Walras)
Auspitz, Rudolf
Lieben, Richard		 Recherches sur la théorie du prix
Bentham, Jeremy Principles of Morals and Legislation
Bertolasi, Ellen Quittner Die Stellung der Lausanner Schule in der Grenznutzenlehre—in Arch. f. Sozialw. u. Sozialpol., 64. Band, Heft 1, August, 1930, pp. 16-44.
Black, J. O. Production Economics
Bonar, James Philosophy and Political Economy
Bousquet, G. H. Essai sur l’évolution de la Pensée économique
Précis de sociologie d’àpres Vilfredo Pareto
Vilfredo Pareto: Sa vie et son oeuvre
Boven, Pierre Les applications mathématiques à l’économie politique
Bowley, A. L. Mathematical Groundwork of Economics
Bridgman, P. W. The Logic of Modern Physics
Cassel, Gustav Theory of Social Economy
Fundamental Thoughts on Economics
Cournot, A. A. The Mathematical Theory of Wealth
Théorie des richesses
Cunynghame, H. Geometrical Political Economy
Del Vecchio, Gustavo La Dinamica Economica Di H. L. Moore—in Giornale degli Economisti, Anno XLV, Giugno, 1930, VIII, No. 6, pp. 545-554.
Dicey Law and Opinion in England
Edgeworth, F. Y. Mathematical Psychics
Papers relating to Political Economy
Evans, G. C. Mathematical Introduction to Economics
Fisher, Irving Mathematical Investigations in the Theory of Value and Prices,—in Transactions of the Connecticut Academy of Arts & Sciences (9-10) pp. 1-125.
Giornale degli Economisti Aug. & Oct., 1924
Halévy, Élie La formation du radicalism philosophique
Hobson, E. W. The Domain of Natural Science
Jevons, W. S. Theory of Political Economy
Journal of the American Statistical Association Dec. 1923; March & Dec. 1924; Dec. 1926 (Papers by H. L. Moore)
Journal of Political Economy Oct. & Dec. 1925; April 1927
Marshall, Alfred Principles of Economics
Industry and Trade
Money, Credit and Commerce
Moore, Henry L. Laws of Wages
Economic Cycles
Forecasting the Yield & the Price of Cotton
Generating Economic Cycles
Synthetic Economics
Moret, Jacques L’emploi des mathématiques en économie politique
Nicol, A. J. Partial Monopoly and Price Leadership (Privately published)
Pantaleoni, M. Pure Economics
Pareto, Vilfredo Manuel d’économie politique
Cours d’économie politique
Anwendung der Mathematik auf National Ökonomie, —in Encycl. Mathematisch, Wissenschaft, I G 2, pp. 1094-1170
Économie mathématique, —in Encyclopédie des sciences mathématique, Tome I, vol. 4 (Fascicule 4, pp. 590-640)
The New Theories of Economics, —in Journ. Polit.Econ., Sept. 1897
Traité de sociologie générale
Pearson, Karl Grammar of Science
Pietri-Tonelli, Alfonso Traité d’économie rationelle
Pigou, Alfred [sic, Arthur] Economics of Welfare
Planck, Max A Survey of Physics
Poincaré, Henri Foundations of Science
Political Science Quarterly Vol. XXXIII, June, 1918, No. 2, pp. 164-5 (Paper by Mitchell)
Quarterly Journal of Economics Jan. 1898; Aug. 1925; Nov. 1926; March 1927
Revue d’histoire des doctrines économique et sociales 1910 (Article by Antonelli on Léon Walras)
Revue d’histoire économique et sociale 1924, pp. 225-43
Revue de metaphysique et de morale (13) 1905 (Section on Cournot)
Ricci, Umberto Die statistischen Gesetze des Gleichgewichtes nach Henry Schultz—in Zeitschrift für Nationalökonomie, January, 1931
Schultz, Henry Statistical Laws of Demand and Supply
Marginal Productivity and the General Pricing Process, —Journ. Polit. Econ., Oct. 1929
Der Sinn der statistischen Nachfragekurven
Vinci, Felice “Sui Fondamenti della Dinamica Economica”, Rivista Italiana di Statistica, Anno II, No. 3, Luglio-Settembre, 1930—VIII, pp. 222-268
Walras, Léon Économie politique appliquée
Économie sociale
Élèments d’économie politique
Wicksteed, Philip The Alphabet of Economic Science
Common Sense of Political Economy
Stephen, Leslie The Utilitarians
Zawadzki, Wl. Les mathématiques appliquées à l’économie politique
Zeuthen, F. L. Problems of Monopoly and Economic Welfare
[handwritten addition] Weinberger, Otto Mathematische Sozialwissenschaft

 

________________________________

Economics 402
Prof. Henry Schultz

REFERENCES ON COST THEORY

Marshall, A.—Principles of Economics, 8th ed., Book V, Chap. V.

Ricci, Umberto—“Curve piane di offerta dei prodotti”, Giornale degli Economisti, Vol. 33, September, 1906, pp. 223ff.

————- “Elasticita dei Bisogni delli Domanda e dell’ offerta,” Giornale degli Economisti, August and October, 1924.

Edgeworth, F. Y.—“The Laws of Increasing and Diminishing Returns”, in Papers Relating to Political Economy, Vol. I, pp. 61-99.

Young, Allyn A.—“Pigou’s Wealth and Welfare”, Quarterly Journal of Economics, Vol. XXVII, 1913, pp. 672ff.

Fanno, Marco—Contributo alla Teoria dell’offerta a costi conqiunti, Rome, 1914.

Clapham, J. H.—“On Empty Economic Boxes”, Economic Journal, Vol. 32, September, 1922, pp. 304-314.

Pigou, Prof. A. C.—“Empty Economic Boxes: A Reply”, Economic Journal, Vol 32, December 1922, pp. 458 ff.

Clapham, J. H.—“The EconomiC Boxes—a Rejoinder”, Ibid.

Knight, F. H.—“Some Fallacies in the Interpretation of Social Costs”, Quarterly Journal of Economics, Vol. 38, 1924, pp. 582ff.

Sraffa, P.—“Sulle relazioni fra costo e quantità prodotta,” Annali di Economia, Bd. II, 1925.

————- “The Laws of Return under Competitive Conditions”, Economic Journal, Vol. 36, December, 1926, p. 535.

Papi, G. U.—Sul costo di produzione nei cicli economica, Rome, 1926.

Del Vecchio, G.—“Il costo quale element della theoria economica,” Giornale degli Economisti, Vol. 67, March, 1926, p. 167.

Robertson, D. H.—“Those Empty Boxes,” Economic Journal, Vol. 34, 1927.

Barone—Grunzüge der theoretischen Nationalökonomie, Bonn, 1927. (Translated by H. Staehle)

Cabiati—“Per riempire alcune ‘empty boxes’ finanziarie,” Giornale degli Economisti, 1928.

Pigou, A. C.—“An Analysis of Supply”, Economic Journal, Vol. 38, June, 1928, p. 238.

Shove, G. F.—“Varying Costs and Marginal Net Products,” Economic Journal, Vol. 38, June, 1928, p. 258.

Robbins, Lionel,–“The Representative Firm”, Economic Journal, Vol. 38, September, 1928, p. 387.

Young, Allyn A.—“Increasing Returns and Economic Progress”, Economic Journal, December, 1928.

Schultz, Henry—Statistical Laws of Demand and Supply, 1928, Chap. IV.

————- “Marginal Productivity and the General Pricing Process”, Journal of Political Economy, Vol. 27, October, 1929, p. 505.

Amoroso, Luigi—“La Curva Statica di offerta”, Giornale degli Economisti, January, 1930.

Robertson, D. H., Shove, G.F., and Sraffa, P.—“Increasing Returns and the Representative Firm: a Symposium”, Economic Journal, Vol. 40, March, 1930, pp. 79ff.

Morgenstern, Oskar—“Offene Problem der Kosten- und Ertragstheorie”, Zeitschrift für Nationalökonomie, Band II, Heft 4, March, 1931, pp. 481ff.

Harrod, R. F.—“Notes on Supply, Economic Journal, Vol. 40, June, 1930, pp. 232 ff.

 

________________________________

Economics 402

Prof. Henry Schultz

REFERENCES ON MONOPOLISTIC COMPETITION

Cournot, A. A.—Mathematical Principles of the Theory of Wealth, (1838) Bacon’s Translation, Chaps. V-VIII.

Edgeworth, F. Y.—Mathematical Psychics, London, 1881, pp. 20 ff.

————- “Teoria pura del monoplio”, Giornale degli Economisti, November, 1897, pp. 13-31.

————- “The Pure Theory of Monopoly” and

————- “Professor Seligman on the Theory of Monopoly”, in Papers Relating to Political Economy, Vol. I, pp. 111-171.

Bertrand, Joseph—“Review of Walras and Cournot”, Journal des Savants, Paris, September, 1883, pp. 499-508.

Marshall, Alfred—Principles of Economics, 8th edition, Chap. XIV.

Pareto, Vilfredo—Cours d’économie politique, 1909, pp. 595-602.

————- Manuel d’économie politique, 1909, pp. 595-602.

————- “Économie mathématique”, Encyclopédie de Sciences mathématiques, Tome I, Vol 4, Fascicule 4 (1911), paragraph 14, pp. 604-608.

Fisher, Irving—“Cournot and Mathematical Economics”, Quarterly Journal of Economics, January, 1898, p. 126.

Moore, Henry L.—“Paradoxes of Competition”, Quarterly Journal of Economics, Vol. XX, 1906, pp. 211 ff.

Zawadski, Wl.—Les mathématiques appliquées à l’économie politique, Paris, 1914, pp. 68-75.

Amoroso, Luigi—Lezioni di Economia mathematica, 1921, pp. 254-272.

————- “La Curva Statica di offerta”, Giornale degli Economisti, January, 1930, especially pp. 11-20.

Edgeworth, F. Y.—Review of Amoroso’s Lezioni, Economie Journal, September, 1922, p. 400.

Clark, J. M.—Economics of Overhead Costs, 1923.

Bowley, Arthur L.—The Mathematical Groundwork of Economics, 1924, p. 38.

Young, Allyn A.—Review of Bowley, Journ. Amer. Stat. Assn., Vol. XX, March, 1925, p. 134.

Myrdal, Gunnar—“Prisbildnings Problemet och Föränderligheten”, Uppsala, 1927.

Wicksell, Knut—“Mathematische Nationalökonomie”, Arch. f. Sozialwiss. u. Sozialpol., 1927, pp. 252 ff.

Schumpeter, Joseph—“Zur Einführung der folgenden Arbeit Knut Wicksells”, Arch. f. Sozialwiss. u. Sozialpol., 1927.

Bowley, A. L.—“Bilateral Monopoly,” Economic Journal, Vol. 38, Dec., 1928, pp. 651 ff.

Schumpeter—“The Instability of Capitalism”, Economic Journal, 1928, pp. 369-70.

Hotelling, Harold—“Stability in Competition”, Economic Journal, Vol. 39, March, 1929, pp. 41-57.

Chamberlin, E. H.—“Duopoly: Value Where Sellers Are Few”, Quarterly Journal of Economics, Vol. XLIV, No. 1, Nov., 1929.

Pigou, Alfred [sic, Arthur]—Economics of Welfare, 3d edition, 1929, Chaps. XIV-XVII.

Evans, G. C.—Mathematical Introduction to Economics, 1930, Chaps. I and III [handwritten note “add solutions (Duopoly)”]

Nichol, Archibald Jamieson—“Partial Monopoly and Price Leadership,” 1930. (Published by the author.)

Schneider, Erich—“Zur Theorie des mehrfachen Monopols, insbesondere der des Duopols”, Archiv. f. Sozialwiss. u. Sozialpol., Vol. 63, Heft 3, 1930, pp. 539-555.

————- “Drei Probleme der Monopoltheorie”, Zeitschrift für Nationalökonomie, Band II, Heft 3, January, 1931, pp. 376-386.

Zeuthen, F.—Problems of Monopoly and Economic Warfare, London, 1930.

 

 

Source: Albert G. Hart Papers. Box 60, Folder “H. Schultz. Math Ec”. Rare Book and Manuscript Library. Columbia University.

Categories
Chicago Exam Questions

Chicago Economics. Ph.D. Exam. Spring 1939

University of Chicago written examination questions. Part I: Economic Theory. Part II: Monetary and Cycle Theory.

 

ECONOMIC THEORY
Written Examination for the Ph.D. Degree

____________________

Spring Quarter, 1939

____________________

PART I

Time: 4 hours

Answer three questions in Group I and three questions in Group II—six questions in all.

____________________

Group I

  1. A competitive industry uses large enough fractions of the available stocks of several important types of productive services appreciably to influence the prices of these services by its own demand for them. Discuss: (a) the probable shape of the long-run supply curve of that industry’s product, and (b) the relationships between (1) that product’s long-run equilibrium price and (2) the long-run average and marginal costs for a particular concern in that industry and also for the industry as a whole.
  2. An industry produces a bulky standardized commodity, e.g., cement, and uses the base-point pricing system. Mill No. 1 is located at a base point which is one hundred miles away from the nearest mill, No. 2, and two hundred miles away from the next mill, No. 3, the three mills being situated in a straight line as follows: 1__________2____________________3. From No. 1 to No. 2 and from No. 2 to No. 3 are separate freight zones, with 25 cents a barrel rates within each zone for any distance, and 50 cents a barrel for shipments from any point in one zone to any point in the next zone regardless of distance. Mill No. 2, however, gets the 25 cents rate for shipment into either zone. You are asked by Mill No. 1 for advice as to (a) how to determine its optimum base point price, and (b) how far it should invade the market territories of Mills Nos. 2 and 3 through freight absorption, maximum net revenue being its sole objective.
    (a) How would you proceed? (What additional information would you need? How would you use it?)
    (b) Do you know of any industries whose price structure is fairly illustrated by this example?
    (c) What objections might be raised against this type of price structure from a social point of view?
  3. Suppose that frequency distributions of hourly money wage rates (a) in different crafts, (b) in different regions, in the United States were constructed for 1910 and for 1930 and that in each case the frequency distribution for 1930 showed a much greater concentration about the mean than the distribution for 1910.
    (a) Frame plausible hypotheses to explain such a trend.
    (b) Indicate in general lines how their validity might be tested.
  4. In a closed economy, with a paper standard currency fixed in quantity, a 10 per cent sales tax levied upon all final sales to consumers of tangible commodities is the only tax. There is substituted for this tax a uniform 15 per cent personal income tax, which produces and identical amount of revenue. Discuss the changes in the price structure which would probably result from the change in the method of taxation.

 

Group II

  1. Discuss the pros and cons of (a) general, and (b) selective, wage-reductions as a means of procuring fuller employment at the present stage of the depression.
  2. Distinguish between “loan-fund,” “cash-balance” (Keynesian), and marginal productivity theories of the determination of the interest rate structure, and discuss the possibility (or the need) of harmonizing them.
  3. Discuss the differences and the resemblances between the objectives and the attitudes toward free economic enterprise of the seventeenth, eighteenth century mercantilists and the present-day advocates of comprehensive economic planning.
  4. Compare the doctrines of the German historical school and the American institutionalists.

Source: Columbia University Archives, Albert Gailord Hart Collection, Box 61, Folder “Sec 2. General Exams Chicago (Micro)”

 

____________________

PART II
MONETARY AND CYCLE THEORY

Written Examination for the Ph.D. Degree

____________________

Spring Quarter, 1939

____________________

Time: 2½ hours.

Answer all four questions.

  1. Explain the doctrine of “forced saving,” and discuss its applicability to the period since 1933.
  2. Discuss and appraise the various parts of the following quotation:
    “If the quantity theory of money is true, the demand for money is taken as perfectly elastic; because human wants are indefinitely extensible, the public’s demand for money is insatiable, and prices vary directly as the quantity of money offerable. When the Austrians began to apply the marginal analysis, this commodity money having unit elasticity—a perfectly flat horizontal demand curve—naturally attracted attention.”
  3. There is a current belief among many economists that investment opportunities for the future will be so restricted as to necessitate continuous spending by governments. Indicate the factors that would have to be considered in deciding upon the merits of this contention and give your conclusion.
  4. Formulate a set of rules in accordance with which you think the gold standard would operate with a considerable degree of acceptability today; or, if you do not believe this to be possible, indicate why. You may assume that a satisfactory redistribution of gold among the nations has been achieved.

Source: Columbia University Archives, Albert Gailord Hart papers, Box 61, Folder “Exams. Chicago.”

Image: University of Chicago Photographic Archive, apf2-07443, Special Collections Research Center, University of Chicago Library.

Categories
Irwin Collier

Somebody noticed

Peter Boettke of the Coordination Problem blog has the first posting  (June 25) in an economics blog to call attention to my Economics in the Rear-view Mirror. And for that first non-selfie signpost in the cloud, my thanks!