For comparison’s sake, here are the questions for the price theory prelim exam at the University of Chicago in 1964.
_________________
PRICE THEORY
Preliminary Examination for the Ph.D. and the A. M. Degree
Winter Quarter, 1969
WRITE THE FOLLOWING INFORMATION ON YOUR EXAMINATION PAPER:
Your code number and NOT your name
Name of examination
Date of examination
Results of the examination will be sent to you by letter
Answer all questions. Time: 3 hours
I.
- A recent survey found that supermarkets in low income areas charge higher average prices than supermarkets in high income areas for many identical items. This is consistent with
_____(a) price discrimination in the sale of groceries
_____(b) no price discrimination
_____(c) lack of competition in the retail grocery market
_____(d) competition in the retail grocery market.
Check those that apply.
On the following questions, indicate whether True (T), False (F), or Uncertain (U), with brief explanation.
- A firm produces output xusing inputs a1 and a2, which it purchases competitively at prices p1 and p2. Its total cost is given by
where A, ?, a1, a2 are constants.
_____(a) The demand for the first factor is given by
_____(b) The production process of the firm exhibits constant returns to scale.
_____(c) The above cost function corresponds to a Cobb-Douglas production function.
- Consider a price system involving four commodities, q1, q2, q3, and q4. If the goods are gross substitutes, it can be shown that the equilibrium will
_____(a) Satisfy the Hicks conditions of perfect stability, and
_____(b) Be dynamically stable.
Assume demand shifts from the first commodity to the second commodity. Again, assuming that the commodities are gross substitutes, it can then be demonstrated that:
_____(c) P1/P2falls and P3/P4remains unchanged;
_____(d) P2/P3rises and P1/P4falls;
_____(e) P3/P1rises by a smaller proportion than P2/P1.
_____ 4. If the consumer’s utility function is separable, then his marginal utility must be declining for all goods.
_____ 5. In a two good world, consumer indifference curves must be everywhere convex to the origin. Otherwise there is no solution to the consumer’s problem of maximizing his satisfaction subject to his budget constraint.
_____ 6. Three top executives leave company A and join company B. The price of company A’s stock falls and the price of company B’s stock rises. This proves that the executives are being exploited.
II.
In Ronald Coase’s celebrated article on the nature of social cost the first example concerns the externality imposed by a cattle ranch that is next to a corn farm. The cattle can wander into the corn farm and eat some of the corn. This increases cost to the corn farmer and imposes an externality on him. Construct a formal analysis of the following situation:
(i) Let there be two firms such that the output of each firm is an “input” in the production function of the other. Let the other inputs be of the same kind, say, labor and capital. Let the output prices be given and let the input prices be given. Derive the profit maximizing solution for the two firms.
(ii) Give a precise measure of the externality and show that the solution in (i) does not depend on who pays whom.
(iii) Under what conditions will the dollar amount of the externality be proportional to the output of the other firm?
III.
Consider an economy with two, L and K, factors of production producing goods, X and Y, under conditions of constant returns to scale. Assume that X is relatively L-intensive at all factor prices.
(a) Analyze the effect of an increase in L on the production of X and Y on the assumption that the relative price of X and Y is constant. How would the increase in L affect the share of L in the economy’s income?
(b) Analyze the effect of an increase in the relative price of X on relative and absolute factor rewards, and on the share of L in the economy’s income. Would your answer be altered if both production functions were of Cobb-Douglas type?
(c) Analyze the effect of an increase in K on the relative price of X on the assumption that neither X nor Y is inferior in the community’s consumption.
IV.
What effect would you expect the British devaluation of the pound from $2.80 to $2.40 to have had on the dollar price of Rolls Royce cars? Justify your conclusion, preferably by diagrams describing the position of the company, indicating explicitly any assumptions you regard as relevant. Assume that wage rates in Britain in pounds are not affected by the devaluation.
V.
The difference between the price of foreign crude oil and the price of domestic crude oil (landed at the same U.S. port) times the quantity of oil consumed in the U.S. is roughly $5 billion. This has been cited as an estimate of the cost to the U.S., in terms of wasted resources, of the whole set of governmental measures special to oil (oil import quotas, percentage depletion allowances, prorationing of oil, etc.). Indicate as specifically as you can the defects, if any, in this measure, and the information needed to set a dollar value on each defect.
Source: Hoover Institution Archives. Papers of Milton Friedman, Box 77, Folder 8 “University of Chicago , Econ 331”.
Image Source: Lecture Hall 1, Social Science Research Building. University of Chicago Photographic Archive, apf2-07482, Special Collections Research Center, University of Chicago Library.