MIT. Advanced Economic Theory Exam, 1962

Coming up will be the reading list(s) and exam for the course Economics 14.123 (Advanced Economic Theory) taught by Robert Solow in the Spring semester of the 1961-62 academic year at M.I.T. 

_____________________

May, 1962

GENERAL EXAMINATION—ADVANCED THEORY

Answer question 1 and 3 others.

1. Make a catalog of the kinds of situations in which resource allocation through the price system is likely to give non-optimal results. Indicate the nature of the non-optimality, and for at least some of the situations describe the analytic reason why non-optimality results.

 

2. A consumer can buy n goods, x₁ … x_n, at prices p₁, … p_n. For each unit of x_i he purchases (for cash), he receives a_i trading stamps. He may then purchase further commodities for trading stamps at fixed trading-stamp prices w₁ … w_n.

Analyze his equilibrium in each of the following cases, interpreting your results in words and explaining how the equilibrium differs (if at all) from the no-trading-stamp equilibrium where all a_i = 0.

(a) a_i = k p_i; w_i = c p_i

(b) a_i = k p_i; w_i ≠ c p_i

(c) a_i ≠ k p_i; w_i = c p_i

(d) a_i ≠ k p_i; w_i ≠ c p_i

 

3. Let A be a non-singular, indecomposable constant Leontief matrix. If this period’s outputs are immediately and exactly plowed back as inputs for next period and there is no capital or consumption:

(a) Set up the implied difference equation system.

(b) Is that system capable of balanced growth?

(c) Under what conditions will it be balanced growth rather than balanced decay?

(d) Is the balanced growth ray unique?

(e) What optimality properties, if any, does balanced growth have?

(f) Is the balanced growth ray stable?

 

4. There are k countries, each with a fixed supply of a single scarce primary factor of production. In country i, it takes a_i units of the factor to produce a unit of wine and b_i units to product a unit of cloth.

(a) Formulate this k-country Ricardian comparative advantage setup as a linear programming problem for world efficiency, and show how the Ricardian results emerge.

(b) State and interpret the dual of the world-efficiency problem.

 

5. An investor has open to him all two-period investment options with net cash flows N₀ and N₁ such that  N₀² + N₁² =1. He can lend unlimited amounts at an interest rate of 4 percent per period and borrow unlimited amounts at a rate of 6 percent per period. His preference for consumption in the two periods C₀ and C₁ are described by the utility function U = C₀ +(C₁)^½. Find the investor’s best plan of action.

 

6. A system uses primary labor and produced capital good(s) to produce consumption output and gross capital formation(s). Labor grows exponentially at the rate of g per annum. Suppose everything else matches that rate of growth. Show that consumption per capita is maximized where the interest rate, r, equals the growth rate, g. (Use any specific model, however simple or complex, to give your proof.)

 

Source: Duke University. Rubenstein Library. Edwin Burmeister Papers. Box 23.

Image Source: MIT beaver from the cover of the 1949 yearbook Technique.