Chicago. Preliminary Graduate Examination in Economic Theory. Winter Quarter, 1963

 

A necessary condition for becoming a certified Chicago economist is to have cleared the hurdle of the prelim exam for price theory. With this post we fill in a gap in our fine collection of price theory prelims that has now grown to a baker’s dozen (i.e. 13).

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Chicago Price Theory
Preliminary/Core Exams
Previously Posted

Summer 1949
Summer 1951
Summer 1952
Winter 1955
Summer 1955
Winter 1957
Winter 1958
Summer 1960
Winter 1964
Winter 1965
Winter 1969
Summer 1975

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CORE EXAMINATION
Price Theory
Winter 1963

Preliminary Examination for the Ph. D. and A.M. Degrees

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.

1. (60 points) Indicate whether you believe each of the following statements to be true, false, or uncertain. In each case write a few sentences explaining your answer. Your grade will depend heavily on your explanation.
   1. If the rate of obsolescence is constant over time for each type of capital equipment, a rise in the rate of interest will shorten the optimal life of capital equipment.
   2. If oranges are substitutes for apples, apples are complementary to cheese, and cheese is a substitute for butter, oranges and butter are complements.
   3. If a certain commodity is rationed and subject to price control, and there is a black market price for it, the black market price is the equilibrium price of the commodity in the absence of price control.
   4. Let Σ_ip_i1x_i1 and Σ_ip_i2x_i2 be the expenditure of a firm on factors of production per unit of output at two points in time. If Σ_ip_i1x_i2 > Σ_ip_i1x_i1 and Σ_ip_i2x_i1 < Σ_ip_i2x_i2, the production function of the firm has changed between the two points of time.
   5. A company cannot have a monopoly if its shareholders receive only the normal rate of earnings on their stock in it.
   6. If the production function of an Industry is subject to constant returns to scale, the industry supply curve will be horizontal.
   7. If it were possible to travel backwards as well as forwards in time, everyone would be a millionaire.
   8. The development of better fertilizer will increase the value of farm land.
   9. Manufacturers frequently advertise that their products contain extra ingredients, and they generally succeed in selling “extra-ingredient” products (e.g. Bufferin) at higher prices than “similar” single-ingredient products (e.g. aspirin). This implies that consumers have a diminishing marginal rate of substitution between the ingredients.
   10. The removal of a barrier to competition anywhere in the economy must make society better off.
   11. Given:
       1. 1. a three-product world,
          2. the cross-elasticity of demand of x with respect to the price of z is zero,
          3. the own-price elasticity of demand for x is -1,
          4. y and z are substitutes,
          5. expenditures on X occupy half of consumers’ budgets, expenditures on Y one quarter of consumers’ budgets in the initial situation,

it follows that the own-price elasticity of demand for y is greater than 1.5 in absolute value. (For this question consider all price-elasticities defined to include the substitution effect only.)

1. 1. 12. The price-elasticity of demand on the part of a competitive industry for a factor of production will be greater, the smaller is the share of that factor of production in the total costs of the industry in question.
      13. If production in industry X (assumed to be competitive) is governed by a Cobb-Douglas production function, then no wage set by the trade union in that industry will produce greater total labor income than any other wage.
      14. A tax of a fixed amount per unit of output, placed upon the product of an industry with constant costs, will necessarily result in a smaller rise in price if that industry is organized (and behaves) as a monopoly than if the industry is competitive.
      15. In an industry employing just two factors of production, the elasticity of demand on the part of that industry for either factor must be less in absolute value than the elasticity of substitution between the two factors in that industry.

2. (15 points) The University City Art Theater, a motion picture house showing foreign films, has the following price policies: The basic admission price is $1.00 for evening performances and 60 cents in the afternoon. Registered university students are admitted at half price at all times. A member of the University’s economics department has complained that the theater is a discriminating monopolist and should be required by local ordinance to follow a one-price policy. Comment on the desirability of this recommendation.
3. (25 points)
   1. Industry X is composed of 10 firms, and organized as a cartel. The pricing policy of the cartel is determined by the following rule: each firm will produce one-tenth of the output of the whole industry, and the price set for the final product will be just equal to the marginal cost of production in the firm with the highest marginal cost. Show how you would measure the welfare cost of this arrangement, as compared with a competitive equilibrium.
   2. The firms now merge into a single monopoly firm, the previous 10 firms now becoming 10 divisions of the new company. All ten divisions continue to operate and have the same marginal cost functions as they did when operating separately. Show how you would measure the welfare costs of this new arrangement. Under what circumstances, if any, would these welfare costs be lower than those of case A?
   3. The government now intervenes to break up the monopoly. The same 10 firms as existed in case A are reconstituted; collusion is somehow prevented; and merger is precluded by a requirement that no firm shall expand the total volume of its capital. Assume that the firms begin operating under this new arrangement with each of them having the amount of capital resulting from a long-run equilibrium under case B, and that the firms behave competitively. How would you measure the welfare costs of this arrangement? Under what circumstances, if any, would these welfare costs exceed those measured under case B?

Source: Harvard University Archives. Papers of Zvi Griliches. Box 130, Folder “Preliminary Examinations, 1957-1965.”