## Johns Hopkins University. Proposal for a course on linear economic systems. Newman, 1968

*The following memorandum written by Peter Newman, the Johns Hopkins mathematical economist (later turned important historian of economics and co-editor of The New Palgrave Dictionary of Economics), provides us with an explicit statement of a theorist’s view of mathematics required of Ph.D. economists in 1968. I find it particularly interesting that no mention of the usefulness of linear algebra for statistics and econometrics was included in his discussion. This memo was found sandwiched in a collection of course reading lists.*

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### DEPARTMENT OF POLITICAL ECONOMY

__Proposed Graduate Course on Theory of Linear Economic Systems__

for discussion on February 21, 1968

- The recent abolition of the University’s second foreign language requirement for the Ph.D. has left the Department in a slight predicament. The mathematics requirement has until now served as a commonly chosen alternative to the second foreign language, and so the latter’s abolition places us under some pressure to drop the former. But we would like all our students to have some mathematics beyond one year of calculus.
- The situation has at least one more complication. Fulfillment of our mathematics requirement normally requires the attending and passing of courses 16 and 19 in the Mathematics Department. There appear to be few problems with 19 (Advanced Calculus), but there is some evidence that 16 (Linear Algebra) is unsuitable, its coverage varying widely from year to year and often having large parts without much relevance to economics.
- I propose the following solution to these difficulties. We should normally require that all students take and pass Mathematics 19. It is better that mathematical analysis be taught by a professional mathematician, and certainly until we have such a person in the Department itself, this course should be taken in the Mathematics Department.
- In addition, it is proposed that all students normally be required to take and pass a one semester 3 hour course on linear economic systems. Prerequisites would be only the usual requirements for graduate admission (courses equivalent to our 301-2, plus one year of calculus), and the course would have a 600 number.
- The levels of economics and mathematics in the course would be approximately those of Dorfman, Samuelson and Solow’s
__Linear Programming and Economic Analysis__, although this is not in fact a very satisfactory textbook. The course would cover such topics as the following:__Mathematical Tools__- Elements of the theory of linear transformations, vectors and matrices, determinants.
- Special matrices of particular relevance to economics, e.g. nonnegative matrices, symmetric matrices, positive definite matrices.
- Elements of linear and nonlinear programming, with a strong focus on duality theory but little on computational aspects.
- Elements of the theory of convex sets and functions.

__Economic Theory__- Models of Leontief type: Theory, and some empirical applications.
- Typical linear programming problems: linear models of production and transportation
- Linear models in welfare economics, general equilibrium, capital accumulation
- Game theory, including a discussion of Von Neumann-Morgenstern utility index.

- It would probably be best if the course were offered each year in the second semester and if it were normally taken by first-year students, who would by then already have had our 601 and Math. 19; this would contribute to the student’s economic and mathematical “maturity”. The course itself could be given by any one of several people in this Department, and the above list of topics is meant only to be typical, not mandatory. If the economic theory were interspersed among the mathematics that would perhaps add to the interest of both, but that is a matter of pedagogy to be decided by the individual teacher.
- At the present time only the more mathematically inclined of our students are exposed systematically to the large body of relevant and recent knowledge covered by such a course. Even if we do not agree (a) that we should have any mathematics requirement at all, or (b) that even if we do, such a course in linear systems would be an appropriate part of the requirement, there would still be a strong case for including this course in the catalogue.

2/13/68

**Source:** Johns Hopkins University, Eisenhower Library. Ferdinand Hamburger, Jr. Archives. *Department of Political Economy Records*, Series 6, Box 1, Folder 3.