M.I.T. General Examination in Economic Theory. May, 1956

[M.I.T.]

GENERAL EXAMINATION
IN ECONOMIC THEORY

May 14, 1956

Answer FIVE questions in all. If you have studied mathematical economics you are urged to take at least one, but not more than two questions from Part II.

PART I

1. “Within the restrictions of static-equilibrium analysis, an increase of demand will normally increase price, whether the good is produced under conditions of pure competition or monopoly.” Explain fully why you agree or disagree.
2. It is sometimes implied that the duopoly problem has a unique solution provided that the duopolists fully recognize their mutual interdependence. What can be said for and against this view?
3. “Under the complex conditions of the real world, marginal productivity concepts are relevant in explaining the factor quantities that an individual firm will use, but those concepts have no relevance in explaining the distribution of income.” Discuss.
4. Treating each situation separately identify the underlying conditions that are implied such that each of the following will be possible:
   1. a redistribution of given total quantities of goods such that all consumers are better off;
   2. a reallocation of given total quantities of factors such that greater quantities of all goods can be produced;
   3. a reallocation of given total quantities of factors such that more of one good and less of another will make all consumers better off;
   4. an increase of the working day such that more goods and less leisure will make all laborers better off.
5. In a truly competitive economy with just two goods (food and clothing) and two factors (labor and land), assume that the food industry is unambiguously the relatively land-intensive one. Supposing now that an innovation makes it possible to produce more food than before with any given factor quantities, discuss the alternatively possible effects on the welfare of both laborers and landlords.
6. It has been suggested that the main result of the pure theory of consumer demand is the following proposition: if demand for a commodity increases when income increases, the demand will also increase when its price falls.
   1. Prove that this proposition is indeed true.
   2. Do you agree that this is the main consequence of the pure theory of demand?
   3. How important a part of economic theory is the theory of demand?
7. An apple orchard and a bee-keeper exist next to each other. The more carefully the orchard is cultivated, the more honey the bees can extract from the blossoms. The more bees there are in the apiary, the more they pollinate the apple blossoms and the higher the yield of fruit. What kinds of misallocations of resources are likely to occur in this situation? How could they be corrected? Does this situation have any important parallel in the modern world?
8. Compare the interest theories of Böhm-Bawerk, Fisher, and Keynes. Are they fundamentally compatible?

Part II

9. Crusoe maximizes

U = ⅓ log x₁ + ⅔ log x₂

subject to
p₁x₁ + p₂x₂ = I

Derive his econometric demand functions.

10. What is the difference between Hicksian stability and “true dynamic stability”? Assuming income effects can be neglected, show that the concepts turn out to be identical.
11. State Euler’s theorem on homogeneous functions and give two or three different economic applications. Show that a Cobb-Douglas function is the only first degree homogeneous function for which relative shares are constant. Deduce the elasticity of demand for labor for a C-D function.

Source: Duke University. David M. Rubenstein Rare Book and Manuscript Library, Economists’ Papers Archive. Paul Samuelson Papers, Box 33, Folder “Teaching Exams. 1952 and 1956”.

Image Source: The M.I.T. beaver featured on the cover the cover of Technique 1949.