Categories
Economists Exam Questions M.I.T. Suggested Reading Syllabus

MIT. Robert Solow’s Advanced Economic Theory Course, 1962

Robert Solow taught the course Advanced Economic Theory at MIT in the Spring of the 1961/62 academic year. Of the dozen graduate students who took the course for credit were a future Nobel prize winner (Peter Diamond), a future Princeton professor and later member of Jimmy Carter’s Council of Economic Advisers (Stephen Goldfeld), a future professor at University of Pennsylvania/Washington University (Robert Pollak), a future professor and later chairman of Hebrew University (David Levhari), and a professor of economics and the first woman to head an MIT academic department, economics! 1984-1990 and MIT’s first female academic dean, School of Humanities and Social Science (Ann Friedlaender).

The three A’s awarded in the course went to Diamond, Levhari and Goldfeld.

The comprehensive exam questions for advanced economic theory from May 1962 were transcribed in the previous post.

_____________________________________

 

14.123—Advanced Economic Theory
Spring 1962—Professor Solow

FIRST READING LIST: LINEAR PROGRAMMING AND RELATED SUBJECTS

This should occupy 6-9 weeks. Most of the reading is in Gale: The Theory of Linear Economic Models and Dorfman, Samuelson, Solow: Linear Programming and Econmic Analysis, referred to below as G and D respectively.

  1. Mathematical background: I hope to avoid spending any time on this. Mainly elements of matrix algebra—14.102 should be enough. For review, see D (Appendix B) and G (Ch. 2, more difficult).
  2. Elements of Linear Programming; D (Ch. 2,3), G (Ch. 1,3).
  3. Algebra and Geometry of Linear Programming, Simplex Method; D (Ch. 4, Sec. 1-11), G (Ch. 4).
  4. Applications; D (Ch. 5-7), Manne: Economic Analysis for Business Decisions (Ch. 4,5).
  5. Two-person zero-sum games; D (Ch. 15), G (Ch. 6,7).
  6. Leontief and similar systems; G (Ch. 8, 9 Sec. 1-3), D (Ch. 9, 10).
  7. Activity analysis; G (Ch. 9, Sec. 4), Koopmans: Three Essays on the State of Economic Science (pp. 66-104).
  8. Von Neumann’s model; D (Ch. 13, Sec. 6), G (Ch. 9, Sec. 5-7).
  9. Sraffa: Production of Commodities by Means of Commodities.
    Robinson: “Prelude to a Critique of Economic Theory”, Oxford Economic Papers, February 1961, 53-58.
  10. If time permits, the turnpike theorem; D (Ch. 12), Hicks: “Prices and the Turnpike”, Review of Economic Studies, February 1961, 77-88.
    Radner: “Paths of Economic Growth that are Optimal, etc.”, Review of Economic Studies, February 1961, 98-104.

(Further references may follow.)

 

SECOND READING LIST: PUBLIC INVESTMENT CRITERIA

  1. Hirshleifer: “On the Theory of Optimal Investment Decision”, Journal of Political Economy, August 1958, pp. 329-352.
  2. Graaff: Theoretical Welfare Economics, Chs. 6-8.
  3. Eckstein: “A Survey of the Theory of Public Expenditure Criteria”, in Public Finances: Needs, Sources and Utilization, with “Comments” by Hirshleifer.
  4. Margolis: “The Economic Evaluation of Federal Water Resource Development”, AER, March 1959, pp. 96-111.
  5. Steiner: “Choosing Among Alternative Public Investments”, AER, Dec. 1959, pp. 898-916.
  6. Maass, al.: Design of Water-Resource Systems, Chs. 2, 13 (and passim).
  7. Eckstein: Water Resource Development, Ch. 1-4.

_____________________________________

April 11, 1962

14.123—Exam

Answer all questions.

  1. A function f of vectors x,y,… is called subadditive if f(x+y) ≤ f(x) + f(y) for all vectors x, y, and called superadditive if the inequality is reversed.
    Consider the LP problem of maximizing C′x subject to Ax ≤ b. The value of the maximum is a function of C, b, and A. Show that it is a subadditive function of C and a superadditive function of b.
  2. A firm can produce n commodities with a linear technology involving one activity for each commodity. Production involves only fixed factors, m in number, m<n, of which specified amounts are available. The output is sold at market prices p, and the firm chooses non-negative vector x of outputs to maximize p′x subject to the fixed-factor limitations.
    (a) Prove that the supply curve is not negatively sloped; that is, prove that if p1 increases, other prices constant, the optimal x1 must increase or remain unchanged, but cannot decrease. (Hint: a straightforward procedure is to consider closely the final simplex tableau, the signs of various elements, and what can happen to require further iteration if p1 There is a much simpler proof, comparing the before-and-after optima.)
    (b) State and interpret the dual to the theorem just proved.
  3. Consider a simple linear model of production, with 2 goods, and with 2 fixed factors, land and labor, available in specified amounts.
    (a) Sketch possible shapes for the set of feasible net outputs, or net production-possibility curve.
    (b) Suppose demand conditions are such that consumption expenditures on the two commodities are always equal. Give a complete analysis of the determination of the prices of the two goods and also the rent of land and the wage of labor. Graphical methods will help. (Hint: at one key point the construction of an isosceles triangle is very useful.)

 

Source: Duke University. Rosenstein Library. Robert M. Solow Papers, Box 67, Folder “14.123 Final Exam Fall-1969[sic|”.

Image Source: Robert Merton Solow at the M.I.T. Museum website.