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Chicago Exam Questions

Chicago. Graduate prelim exam questions for price theory, 1969

 

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.

  1. 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.

  1. A firm produces output xusing inputs aand a2, which it purchases competitively at prices pand p2. Its total cost is given by

C=A{{x}^{\gamma }}p_{1}^{{{a}_{1}}}p_{2}^{{{a}_{2}}}

where A, ?a1, aare constants.

_____(a) The demand for the first factor is given by

{{a}_{1}}=\frac{\partial C}{\partial {{p}_{1}}}=\frac{{{\alpha }_{1}}C}{{{p}_{1}}}

_____(b) The production process of the firm exhibits constant returns to scale.

_____(c) The above cost function corresponds to a Cobb-Douglas production function.

 

  1. 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, and K, factors of production producing goods, and Y, under conditions of constant returns to scale. Assume that is relatively L-intensive at all factor prices.

(a) Analyze the effect of an increase in on the production of and on the assumption that the relative price of and is constant. How would the increase in affect the share of in the economy’s income?

(b) Analyze the effect of an increase in the relative price of on relative and absolute factor rewards, and on the share of 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 on the relative price of on the assumption that neither nor 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.