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Harvard. Application for PhD candidacy and graduate records. Olin Winthrop Blackett, 1926

The first two items posted below from the graduate records of Olin Winthrop Blackett (Harvard PhD 1926) are of particular significance, marking what appears to be the very first time that Mathematics was accepted as a field in the General Examination for a PhD in economics at Harvard. The decision to accept Mathematics as a minor field was made in November 1920, Blackett’s general examination took place in May 1922 and his PhD was awarded in 1926. The title of Blackett’s doctoral thesis was “The Cyclical Movements of the Prices of Raw materials in the Iron and Steel Industry.”

 

_________________________

Requesting approval of a mathematics minor in the General Examination

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

F. W. Taussig
T. N. Carver
W. Z. Ripley
C. J. Bullock
A. A. Young
W. M. Persons
E. E. Day
J. S. Davis
H. H. Burbank
A. S. Dewing
E. E. Lincoln
A. E. Monroe
A. H. Cole		  

 

 

 

Cambridge, Massachusetts

November 5, 1920

Prof. C. H. Haskins,
Harvard University,
Cambridge, Mass.

Dear Mr. Haskins,

I enclose herewith O. W. Blackett’s application for candidacy for the degree of Ph.D. in Economics. Blackett’s program is perfectly regular with the possible exception of the offering Mathematics as his minor. It seems to me that even in this particular the program is normal. I have talked over the Mathematics minor with the Department of Mathematics, particularly with Professor Huntington and have come without difficulty to an understanding which seems to assure a minor in that Department fully the equivalent of any of the other more common minors, and particularly serviceable for men who propose to specialize, as does Blackett, in the field of Statistical Method.

If Blackett’s program is approved, one or two others of similar kind will be submitted at an early date. I doubt not, furthermore, that Mathematics minors will become common among those expecting to specialize along statistical lines. Statistical method clearly is developing in directions that make a sound mathematical training an indispensable element in an adequate professional equipment.

Should Mathematics be accepted for men specializing in Statistics, I would suggest that you try to obtain the services of Professor Huntington as examiner when the field is up at the General Examinations. Professor Huntington has a definite interest in the application of Mathematics to Statistical Methode and is thoroughly acquainted with the material upon which candidates in Economics may most profitably be examined.

Sincerely yours,
[signed] Edmund E. Day

EED A
Encl.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Request Granted

8 November 1920

Dear Day:

I cordially approve of Blackett’s programme, with the explanation given in your letter. It seems to me that when we accept Mathematics, we should be sure of men’s general Economics preliminary training, and that these men in particular get the courses in Economic History. Our plans ought always to be flexible enough to include the acceptance of an outside subject, where it is essential to the student’s work. What you say about the necessity of Mathematics for statisticians is sound, and I hope we shall encourage other men to take the same field. I shall bring the plan up at the next meeting of the Division.

Sincerely yours,
[unsigned copy of C. H. Haskins]

Professor E. E. Day.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

HARVARD UNIVERSITY
DIVISION OF HISTORY, GOVERNMENT, AND ECONOMICS

Application for Candidacy for the Degree of Ph.D.

[Note: Boldface used to indicate printed text of the application; italics used to indicate the handwritten entries]

I. Full Name, with date and place of birth.

Olin Winthrop Blackett. July 12, 1895. Winthrop, Mass.

II. Academic Career: (Mention, with dates inclusive, colleges or other higher institutions of learning attended; and teaching positions held.)

Wesleyan University, 1914-17, & 1919-20.
Rich Fellow and Assistant in Economics, Wesleyan, 1919-20.

III. Degrees already attained. (Mention institutions and dates.)

B.A. Wesleyan, 1917.
M.A. Wesleyan, 1920.

IV. General Preparation. (Indicate briefly the range and character of your undergraduate studies in History, Economics, Government, and in such other fields as Ancient and Modern Languages, Philosophy, etc. In case you are a candidate for the degree in History, state the number of years you have studied preparatory and college Latin.)

Economic Theory —1 year elementary —3 years advanced.
Money and Banking —1 year. Corporations —1 year.
Tariff and International Trade —1 year. Labor Prob. —1 year.
Socialism, Single Tax, etc. —2 years. Statistics — 1 year.
American History —1 year. English & European History —1 year.
Philosophy —2 years. German —2 years. Math —4 years.

V. Department of Study. (Do you propose to offer yourself for the Ph.D., “History,” in “Economics,” or in “Political Science”?)

Economics

VI. Choice of Subjects for the General Examination. (State briefly the nature of your preparation in each subject, as by Harvard courses, courses taken elsewhere, private reading, teaching the subject, etc., etc.)

  1. Economic Theory. — This was my major study during three years of undergraduate work and one year of work for the masters degree. Taught theory 1 year in Wesleyan U. Eco. 11 & 14 at Harvard this year.
  2. Money, Banking, and Crises. — 1 year course in Wesleyan University. Auditor in Eco. 3 this year.
  3. Public Finance. — Eco. 31 this year at Harvard.
  4. Statistics. — 1 year in Wesleyan University. Private study during the summer of 1920.
  5. Economic History. — Studied in connection with courses in economics and history in Wesleyan U. Econ. 2a & 2b this year at Harvard.
  6. Mathematics. — 4 years work in Wesleyan U. including algebra, trig. analytic geom., calculus, finite differences, reduction of observations, interpolation, theory of errors, least squares, moments. 

VII. Special Subject for the special examination.

Statistics

VIII. Thesis Subject. (State the subject and mention the instructor who knows most about your work upon it.)

The Machine Tool Industry. Cyclical Price Movements of Raw Materials in the Iron and Steel Industry.
Prof. Persons.

IX. Examinations. (Indicate any preferences as to the time of the general and special examinations.)

As late as possible in the spring of 1921 for the general examination.

X. Remarks

 [left blank]

Signature of a member of the Division certifying approval of the above outline of subjects.

[signed] Edmund E. Day — Chairman

*   *   *   [Last page of application] *   *   *

[Not to be filled out by the applicant]

Name: Olin W. Blackett.

Approved: January 25, 1921.

Ability to use French certified by C. J. Bullock. 3 March, 1922.

Ability to use German certified by  C. J. Bullock. 3 March, 1922.

Date of general examination May 19, 1922. Passed.

Thesis received October, 1925.

Read by Professors Persons, Crum, and Young.

Approved November 1925.

Date of special examination Monday. April 12, 1926.

Recommended for the Doctorate [left blank]

Degree conferred [left blank]

Remarks.  Mr. O. W. Blackett was examined on Monday, April 12, at 4 p.m. in room 404 College House by Professors Persons (chairman), Crum, Huntington and W.M. Cole. The committee unanimmously voted that the examination be accepted as satisfactory.
[signed] Warren M. Persons, Chairman.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Postponing General Examination from Spring to Fall 1921

15 Park Vale
Brookline, Mass.,
March 2, 1921

My dear Miss Cogswell:

Please pardon the delay in returning the copy you sent me. The material is as complete as I am able to make it at the present time. I shall not be a candidate for the General Examination this spring but shall present myself probably in the fall.

Yours truly,
[signed] Olin W. Blackett.

[NOTE: The General Examination was in fact postponed to the following Spring, May 19, 1922]

  *  *  *  *  *  *  *  *  *  *  *  *  *

Draft of Planned General Examination Announcement (undated)

OLIN WINTHROP BLACKETT.

GENERAL EXAMINATION in Economics

COMMITTEE [left blank].

ACADEMIC HISTORY: Wesleyan University, 1914-17, 1919-20; Harvard Graduate School, 1920-. A.B., Wesleyan, 1917; A. M., ibid., 1920. Assistant in Economics, Wesleyan University, 1919-20.

GENERAL SUBJECTS: 1. Economic Theory. 2. Money, Banking, and Crises. 3. Public Finance. 4. Statistics. 5. Economic History. 6. Mathematics.

SPECIAL SUBJECT: Statistics.

THESIS SUBJECT: [left blank].

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Certification of reading knowledge
of French and German

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

F. W. Taussig
T. N. Carver
W. Z. Ripley
C. J. Bullock
A. A. Young
W. M. Persons
E. E. Day
H. H. Burbank
A. S. Dewing
J. H. Williams
A. E. Monroe
A. H. Cole
R. S. Tucker
R. S. Meriam		  

 

 

 

Cambridge, Massachusetts

March 3, 1922

Dear Haskins:

This certifies that I have examined Mr. O. W. Blackett and find that he has such a reading knowledge of French and German as we require of candidates for the Degree of Philosophy [sic].

Very truly yours,
[signed] Charles J. Bullock

Dean C. H. Haskins

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Date and Place of General Examination

16 May 1922

My dear Mr. Blackett:

Your General Examination on Friday, 19 May, will be held in Widener U at 4 P.M.

Very truly yours,
[unsigned copy]
Secretary of the Division

Mr. O. W. Blackett.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Committee of General Examination

23 May 1922

My dear Sir:

Your general examination will come Friday, 19 May, unless otherwise notified. Professors Day, Huntington, Young, Burbank, and Dr. Clark, have ben appointed to examine you. Of course, the committee is tentative, not final.

Very truly yours,
[unsigned copy]
Secretary of the Division

Mr. O. W. Blackett.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

General examination passed

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

F. W. Taussig
T. N. Carver
W. Z. Ripley
C. J. Bullock
A. A. Young
W. M. Persons
E. E. Day
H. H. Burbank
A. S. Dewing
J. H. Williams
A. E. Monroe
A. H. Cole
R. S. Tucker
R. S. Meriam		  

 

 

 

Cambridge, Massachusetts

May 22, 1922

Dear Young,

For the purposes of final record may I report that Mr. Olin W. Blackett’s General Examination in Economics was conducted on the afternoon of the 19th by the following Committee: Professors Day (chairman), Huntington, Young, Burbank,and Dr. Clark. This Committee voted unanimously that the examination be accepted. I return herewith the papers covering Mr. Blackett’s candidacy.

Very truly yours,
[signed by “K” for] E. E. Day

Professor A. A. Young

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Special Examination Date
When exactly?

Februrary 1, 1926

My Dear Mr. Blackett:

Mr. Robinson, the Secretary of the Graduate School, has communicated to me the contents of your letter to him in which you say that vou will not be able to reach Cambridge until April 12. Do you mean thet you would like to have your special examination on that date, or on some day later in the month? Your thesis has been approved.

Very truly yours,
[unsigned Gladys E. Campbell]
Secretary.

Mr. O. W. Blackett

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Request for Special Examination during week of April 12th

University of Michigan
Ann Arbor
School of Business Administration

February 4, 1926.

Miss Gladys E. Campbell
Div. of History, Gov. and Econ.
Harvard University
Cambridge, Mass.

My dear Miss Campbell,

I have your letter of February 1st and would appreciate it very much if you would make arrangements for my special examination in Statistics during the week of April 12th.

Very truly yours,
[signed] O. W. Blackett

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Request to Confirm Special Examination during week of April 12th

University of Michigan
Ann Arbor
School of Business Administration

March 18, 1926.

Miss Gladys E. Campbell
Div. of History, Gov. and Econ.
Harvard University
Cambridge, Mass.

My dear Miss Campbell,

I have not heard from you whether arrangements have been made for my special examination in Statistics during the week of April 12th. Would you let me know as soon as final arrangements can be made?

Very truly yours,
[signed] O. W. Blackett.

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Date and Committee
for Special Examination

March 18, 1926.

My dear Mr. Blackett:

I have your note of March 13 asking if arrangements had been made for your special examination. The date has been arranged for April 12 at four o’clock and the committee consists of Frofessors Persons (chairman), Crum, Cole, and Huntington. The place will be named later.

Letters addressed to Professor Haskins or to me will reach us more quickly if sent to 774 Widener Library.

Very truly yours,
[unsigned Gladys E. Campbell]
Secretary of the Division.

Mr. O. W. Blackett

*  *  *  *  *  *  *  *  *  *  *  *  *  *

Record of Olin Winthrop Blackett in the
Graduate School of Arts and Sciences
(2 November 1925)

1920-21
Grades
Course Half-Course
Economics 2a1 B
Economics 2b2 C
Economics 11 A
Economics 14 A minus
Economics 31 A
1921-22
Grades
Course Half-Course
Economics 151 A
Economics 41 A
1922-23
Grades
Course Half-Course
Economics 20 A
1923-24
Grades
Course Half-Course
Economics 20 (1st half) A

Source: Harvard University Archives. Division of History, Government & Economics. PhD. Examinations, Box 6: 1924-26.

__________________________

Course Names and Instructors

1920-21

Economics 2a 1hf. European Industry and Commerce in the Nineteenth Century. Dr. E. E. Lincoln assisted by Mr. Hyde.

Economics 2b 2hf. Economic and Financial History of the United States. Dr. E. E. Lincoln assisted by Mr. Hyde.

Economics 11. Economic Theory. Professor Taussig.

Economics 14. History and Literature of Economics to the year 1848. Professor Bullock.

Economics 31. Public Finance. Professor Bullock.

1921-22

Economics 15 1hf. Modern Schools of Economic Thought. Professor Young.

Economics 41. Statistical Theory and Analysis. Professor Day.

1922-23, 1923-24

Economics 20. Economic Research.

Source: Harvard University. Report of the President of Harvard College for 1920-21. Faculty of Arts and Sciences, Announcements of the Courses of Instruction, 1921-22.

__________________________

Olin Winthrop Blackett
His life and career

Olin Winthrop Blackett, Obituary

Olin Winthrop Blackett, born July 12, 1895 in Winthrop, MA, died peacefully on Sept. 12, 1993 [sic, September 7 is correct] in Tacoma, WA. He attended Wesleyan University, the United States Naval Academy and served in the U.S. Navy in World War I. He received a PhD in economics from Harvard University where he continued on to teach in the Harvard Business School. He moved to Ann Arbor, MI, in 1924 where he was Professor of Business Statistics at the University of Michigan Business School until his retirement in 1965. He then lived in Key Alegro, TX until the death of his wife, Ruth E. Blackett in 1978 when he moved to Tacoma…

Source: The News Tribune (Tacoma WA) 9 September 1995

Image Source: Portrait from the Anne Olson family tree, “Olin Winthrop Prof. Blackett” at ancestry.com

Categories
Exam Questions Math Princeton

Princeton. Mathematics for Economics Grad Students Exam. 1960

Before one gets too smug about the modest level of mathematical sophistication revealed in the following examination that was taken in 1960 by ten Princeton economics graduate students and only passed by half of them, it is important to keep in mind that the purpose of the examination appears only to have been to permit economics students to substitute mathematics for a foreign language as a formal requirement to be awarded a Ph.D. degree. As far as I am aware, by 1960 the exams to test a reading knowledge of a foreign language (at least those administered by an economics department itself) were rather low hurdles hardly capable of tripping any diligent student and generally a waste of time for all but the area specialists and economic historians. Still five of the ten economics grad students at Princeton failed the mathematics exam transcribed below!

__________________________

On Harold W. Kuhn

Princeton University obituary for Harold W. Kuhn (1925-2014).

Autobiographical sketch in WIKIMIZATION.

__________________________

MEMORANDUM

To: Members of the Economics Department
From: H. W. Kuhn
Re: Mathematics Examination for graduate students.

Attached is a copy of the first Mathematics Examination for graduate students in Economics which, as you know, can substitute for one language examination. This memorandum is to describe what the examination was intended to test, report on the performance of the students who took it, and invite comments from you concerning the design of future examinations. (Will Baumol is writing the next one now.)

By agreement of those charged with the conduct of the examination (Baumol, Coale, Kuhn, Okun, and Quandt), it deals only with two subjects, calculus and matrix algebra. The level of the calculus that is assumed is thoroughly elementary and could be acquired in a one-year course. However, it should be augmented by those calculus tools peculiar to economics such as Lagrange multipliers, partial derivatives, and optimization conditions. Study of R. G. D. Allen’s “Mathematical Analysis for Economists” is recommended. The level of matrix algebra is harder to specify. Almost any standard course is too much. Two indications of the level of proficiency demanded are the matrix algebra sections of “Finite Mathematics” by Kemeny, Snell, and Thompson or the Appendix to Dorfman, Samuelson, and Solow. Another book appropriate for study would be “Mathematical Economics” by R. G. D. Allen

The following is an explanation of the first test, question by question, with remarks on the performance of the ten students who took it.

  1. Straightforward translation of economic terms from words to formulas and back. Four parts out of five was par for the course.
  2. The definition of matrix multiplication and of a production matrix. All answers were correct.
  3. A test of understanding of the first and second order conditions for a maximum. Very poor performance; much confusion between necessary and sufficient conditions.
  4. A test of their acquaintance with an indispensable mathematical tool, the Lagrange multiplier. The first pages of “Value and Capital” will give an example. Good performance.
  5. This was intended to draw out the linear case in which solvability is stated in matrix terms. Good performance.
  6. The proper method was by means of partial differentiation. From the variety of answers (mostly weak), this should have been clued.
  7. This model is reproduced almost verbatim from “Finite Mathematics.” The question is intended to test the ability to translate matrix relations into meaningful economic conditions. The average was about half right.

The test was graded on a strict percentage basis, with 70% a passing grade. Five passed and five failed. This may be somewhat hard on those who failed but reflects my own belief that requirements are better too hard than so easy as to be meaningless.

COMMENTS INVITED

__________________________

PRINCETON UNIVERSITY

Department of Economics
Mathematics Examination

October 26, 1960

Please spend no more than two hours on this examination. No books or papers may be consulted. Please attempt all of the questions.

  1. Let y = f(z) be a production function, where y denotes the quantity of output for a quantity of input z. Let c = g(y) be the associated cost function. Let P = F(y) define the demand schedule.

Give the common names for

    1. dy/dz
    2. dc/dy
    3. Py

Give formulas for the

    1. marginal revenue
    2. price elasticity of demand.
  2. The number of tubes and the number of speakers used in assembling three different models (a), (b), (c) of TV sets are specified by a parts-per-set matrix.

\begin{gathered}\\ \begin{matrix}(a)&(b)&(c)&\  \  \  \  \  \  \  \ \end{matrix}\\ \left[ \begin{matrix}13&18&20\\ 2&3&4\end{matrix} \right] \begin{matrix}\text{tubes}\\ \text{speakers}\end{matrix}\end{gathered}

The number of orders received for the three different models in January and February are specified in a sets-per-month matrix

\begin{gathered}\begin{matrix}\  \  \ &\text{Jan.}&\text{Feb.} \  \ \end{matrix}\\ B=\  \left[ \begin{matrix}12&6\\ 24&12\\ 12&9\end{matrix} \right] \begin{matrix}(a)\\ (b)\\ (c)\end{matrix}\end{gathered}

Express the number of parts used per month as a matrix C in terms of A and B. How many tubes were used in February?

  1. Let y = f (x) be a differentiable function defined for

a ≦ x ≦ b. Let a < c < b.

    1. The conditions f'(c)=0 and f”(c)< are necessary and sufficient for f(c) to be a local maximum value for f. True or false? (Give explanation.)
    2. Describe a method for finding the absolute maximum value of f.
  1. Lagrange multipliers are used to solve what class of calculus problems? Give at least one example from economic theory.
  2. Discuss the assertion: Every system of n equations in n unknowns has a unique solution. (It is clearly false; show this by example and modify the statement to be useful.)
  3. The following formula gives the profit P in dollars as a function of the quantities x1, and x2 of two commodities.

P = x150 x235 + x185

When x1 = x2 = 100, P = 2 • 10170
Approximate P when x1 = 101 and x2 = 100

  1. Consider the following economic model: A set of n goods are produced (jointly by m activities. The ith activity requires aij units of good j and produces bik units of good k.
    Let x = (x1,…,xm) represent the levels of the activities
    and yt = (y1,…,yn) represent the prices of the goods, while A and B denote the input and output matrices. Suppose α and β are non-negative numbers. Give common English interpretations of the following equilibrium conditions:

    1. x (B – α A) ≧ 0
    2. (B – β A) y ≦ 0
    3. x (B – α A) y = 0
    4. x (B – β A) y = 0
    5. x B y > 0

What condition on A would insure that every process uses some good as input?
What condition on B would insure that every good can be produced in the economy?

Source:  Duke University. David M. Rubenstein Rare Book & Manuscript Library. Economists’ Papers Archive.  William J. Baumol Papers, Box 10, Folder “Princeton University 1952-69”.

Image Source: Harold W. Kuhn, ca. 1961. Wikimization website.

Categories
Harvard M.I.T. Math Pedagogy Princeton Teaching Wisconsin

Harvard. Draft memo on “Basic Mathematics for Economics”. Rothschild, ca. 1970

 

“These bewildering cook-books [Allen, Lancaster, Samuelson, Henderson & Quandt] are as helpful to those without mathematical training as Escoffier is to weekend barbecue chefs.”

The 1969 M.I.T. economics Ph.D. Michael Rothschild served briefly as assistant professor of economics at Harvard, a professional milestone that went somehow unmentioned in his official Princeton biography included below. He co-taught the core graduate microeconomic theory course with Zvi Griliches in the spring term of 1971 which is probably why a draft copy of his memo proposing  “a course which truly covers ‘Basic Mathematics for Economists'” is found in Griliches’ papers at the Harvard Archives.

Tip: Here is a link to an interview with Michael Rothschild posted in YouTube (Dec. 4, 2012). A wonderful conversation revealing his academic humility and wit as well as an above-average capacity for self-reflection.

_________________________________

Courses Referred to in Rothschild’s Memo

Economics 199. Basic Mathematics for Economists

Half course (fall term). M., W., F., at 10. Professor G. Hanoch (Hebrew University).

Covers some of the basic mathematical and statistical tools used in economic analysis, including maximization and minimization of functions with and without constraint. Applications to economic theory such as in utility maximization, cost minimization, and shadow prices will be given. Probability and random variables will be treated especially as these topics apply to economic analysis.

Source: Harvard University, Faculty of Arts and Sciences. Courses of Instruction, Harvard and Radcliffe 1969-1970. Published in Official Register of Harvard University, Vol. LXVI, No. 12 (15 August 1969), p. 142.

*  *  *  *  *  *  *  *

Economics 201a. Advanced Economic Theory

Half course (fall term; repeated spring term). Tu., Th., (S.), at 12. Professor D. Jorgenson (fall term); Professor W. Leontief (spring term).

This course will be concerned with production theory, consumption theory, and the theories of firms and markets.
Prerequisite: Economics 199 or equivalent.

Source: Ibid., p. 143.

*  *  *  *  *  *  *  *

Economics 221a. Quantitative Methods, I

Half course (fall term; repeated spring term). Tu., Th., S., at 11. Assistant Professor A. Blackburn (fall term); Assistant Professor M. Rothschild (spring term).

Probability theory, statistical inference, and elementary matrix algebra.

Prerequisite: Economics 199 or equivalent

Source: Ibid., p. 146.

_________________________________

DRAFT
[Summer or Fall 1970?]

M. Rothschild

Economics 201a, as Professor Jorgenson now teaches it1, presumes much specialized mathematical knowledge. (See attachment 1) There is no single course which covers all these topics, (chiefly the implicit function theorem, constrained maximization and Euler’s theorem), in either the economics or mathematics departments at Harvard. We are in effect demanding that our students arrive knowing these things or that they learn them on their own. The former is unlikely, the latter more so. Imagine trying to learn the mathematics necessary to follow the standard derivation of the Slutsky equation by studying the standard sources such as Allen, Mathematical Analysis for Economists, Lancaster’s Mathematical Economics or the appendices to Samuelson’s Foundations or Henderson and Quandt. These bewildering cook-books are as helpful to those without mathematical training as Escoffier is to weekend barbecue chefs. Those with some knowledge of mathematics will not find the standard sources much more helpful for they are written in a spirit alien to that of modern mathematics; they give almost no motivation or intuition for their results.

There are other bits of mathematics necessary for a thorough understanding of basic economic theory. For instance, the stability theory of difference and differential equations, the theory of positive matrices and rudiments of duality and convexity theory are required for the stability analysis of simple macro models, input output economics, and linear programming respectively. These are hardly new fangled and abstruse parts of economic theory. Indeed they are topics which should be part of every economist’s competence.

There are courses at Harvard where one can learn these things; the difficulty is that there are so many. Advanced courses in mathematical economics treat of positive matrices, duality and much more. Few students take these courses and almost no first year students do. I have no doubt that somewhere in the mathematics or applied math department, there is a course where one may learn all one would want to know and more of difference and differential equations. But all economists really need to know can be taught in three weeks or less.2

There is an obvious solution to these problems, namely for the department to offer a course which truly covers “Basic Mathematics for Economists.”3 A proposed course outline is attached. The course begins with linear algebra because most of the specialized topics needed for mathematical economics are applications of the principles of linear algebra. I know of no one semester course at Harvard which teaches linear algebra in a manner useful to economists. Another advantage to including linear algebra in this course is that it would make it possible to drop the topic from Economics 221a which is presently supposed to teach linear algebra, probability theory, and statistics in a single semester.4 I doubt this can be done. If linear algebra were excluded from the syllabus of 221a, there would be less reason for offering the course in the economics department. We could reasonably expect that our students learn statistics and probability theory from the statistics department (in Statistics 122, 123 or 190).

*  *  *  *  *  *

1…and, I hasten to say, as it should be taught

2A word must be said here about Mathematics 21. This excellent full year course in linear algebra and the calculus of several variables contains all the insights, and almost none of the material, which economists should know. With a slight rearrangement of topics, principally the addition of the implicit function theorem, constrained maximization, and the spectral theory of matrices this would be a great course for economists. As it is now it is a good, but rather time consuming, way to develop mathematical maturity which should make it easy to learn the mathematical facts economists need to know.

3The present title of Economics 199 which is a remedial calculus course taken only by those students with almost no mathematical training.

4I became aware of the need for such a course while teaching 221a. After spending three very rushed weeks developing some of the basic notions of linear algebra I had to drop the subject just when it would have been easy to go on and explain the mathematics behind basic economic theory. The desire of the students that I do so is indicated by the fact that most of them were enticed to sit through a second (optional) hour of lecture on a Saturday by the promise that I would unravel the mysteries of the determinental second order conditions for maximization of a function of several variables.

*  *  *  *  *  *

Proposed course outline:
  1. Linear Algebra, vector spaces, linear independence, bases, linear mappings, matrices, linear equations, determinants.
  2. Cursory review of the calculus of several variable from the vector space point of view, the implicit function theorem, Taylor’s theorem.
  3. Quadratic forms and maximization with and without constraints; diagonalization, orthogonality and metric concepts, projections.
  4. The Theory of Positive matrices; matrix power series.
  5. Linear Difference Equations, stability.
  6. Linear Differential Equations, stability.
  7. Convex sets and Duality. (If time permits.)

_________________________________

Michael Rothschild

Mike Rothschild first came to Princeton in 1972 as a lecturer in economics and quickly rose to the rank of professor three years later. Mike is an economist with broad interests in social science. His 1963 B.A. from Reed College was in anthropology, his 1965 M.A. from Yale University was in international relations, and his 1969 Ph.D. from the Massachusetts Institute of Technology was in economics.

In the early 1970s, Mike published a string of ground- breaking papers studying decision making under uncertainty and showing the effects of imperfect and asymmetric information on economic outcomes. With Joseph Stiglitz, Mike proposed now- standard definitions of what it means for one random variable to be “riskier” than another random variable. He studied consumer behavior when the same good is offered at different prices and when the consumer does not know the distribution of prices. He studied the pricing behavior of fi when they are uncertain about demand and showed that a fi may end up setting the wrong price even when it optimally experiments to learn about the demand for its product. Arguably, Mike’s most important early work was a 1976 paper with Stiglitz on insurance markets in which insurance companies did not know the heterogeneous risk situations of their customers. Mike and Stiglitz showed that under certain circumstances a market equilibrium exists in which companies offer a menu of policies with different premiums and deductibles that separate customers into appropriate risk groups. This research is one of the landmarks in the field of information economics.

Mike left Princeton in 1976 for the University of Wisconsin and moved to the University of California–San Diego (UCSD) seven years later. His research over this period included papers on taxation, investment, jury-decision processes, and several important papers in finance. Mike’s research contributions led to recognition and awards: he became a fellow of the Econometric Society in 1974, received a Guggenheim Fellowship in 1978, became a fellow of the American Academy of Arts and Sciences in 1994, and in 2005 was chosen as a distinguished fellow of the American Economic Association.

In 1985, Mike decided to branch out from teaching and research, and he spent the next 17 years in university administration. Shortly after arriving at UCSD he became that university’s first dean of social sciences. Under his watch, the division grew dramatically in the number of students, faculty, departments, and programs. He presided over the launching of cognitive science, ethnic studies, and human development. During his deanship, the UCSD social sciences soared in the national rankings, reaching 10th nationally in the last National Research Council tally for 1996.

Mike was lured back to Princeton in 1995 to become the dean of the Woodrow Wilson School of Public and International Affairs. During his seven-year tenure as dean, Mike started the one-year Master in Public Policy program for mid-career professionals; the Program in Science, Technology, and Environmental Policy; the Center for the Study of Democratic Politics; and the Center for Health and Wellbeing. Under his leadership, the Wilson School added graduate policy workshops to the curriculum, expanded course offerings, added multi-year appointments of practitioners to the faculty, and enhanced professional development. Mike shared his dean duties with his trusted and loyal dog, Rosie, who became an important part of the school’s community and accompanied Mike throughout campus.

Finally, Mike likes to wear a hardhat. At UCSD he oversaw the planning and construction of the Social Sciences Building, and at Princeton he built Wallace Hall and renovated Robertson Hall. The Princeton community may remember Mike most for turning Scudder Plaza from the home of a formal reflecting pool where guards kept people out of the fountain into a community wading pool that welcomes and attracts students, families, and children (many under the age of three) each summer evening.

Source: Princeton University Honors Faculty Members Receiving Emeritus Status (May 2009), pp. 18-20.

Image Source: Screenshot from the interview (Posted Dec. 4, 2012 in YouTube).