MIT. Microeconomic Core Theory II. Bishop, 1974

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“Microeconomic Theory II”, the second of four half-semester core microeconomic theory courses at MIT, was actually the first offered during the academic year 1974-75. It was taught by Professor Robert L. Bishop. In this post we find 29 sample questions for the five sets of topics covered in the courses. Also included are the waiver exam for testing out of the course and the final examination for the students who took the course

The course “text” was the mimeographed manuscript on economic theory written by Bishop that was on closed reserve at Dewey Library and consulted by presumably at least a dozen cohorts over the 1960s (perhaps even earlier) and 1970s. A copy of that manuscript can be found in the Edwin Burmeister papers at Rubenstein Library of Duke University. 

 Two papers (especially the second) by Bishop covering some of the course material are:

Bishop, Robert L. “Duopoly: Collusion or Warfare?” The American Economic Review 50, no. 5 (1960): 933-61.

Bishop, Robert L. “The Effects of Specific and Ad Valorem Taxes.” The Quarterly Journal of Economics 82, no. 2 (1968): 198-218.

Core microeconomic theory at MIT in 1974-75:

14.121 (linear models) was taught by Martin Weitzman,
14.123 (duality) was taught by Hal Varian,
14.124 (capital theory, uncertainty and welfare economics) was taught by Paul Samuelson.

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Topics in 14.122, with Sample Questions

1. Review of demand and supply, elasticities. Walrasian v. Marshallian stability conditions. Demand and supply as seen by the individual seller or buyer.
   1. What various formulas have been proposed for measuring the arc elasticity between two points on a demand curve, (q₁,p₁) and (q₂,p₂)? Discuss the virtues and defects of the various definitions. Can any one be said to be “best”?
   2. Compare the Walrasian and Marshallian stability conditions as to (a) their content, (b) the types of markets in which they are realistically applicable, and (c) the situations in which they do not agree.
   3. If 1000 sellers have fixed supplies of 50 units each of a good, how does the demand confronting each individual seller relate to the market demand (a) as to slope, (b) as to elasticity? How are the answers affected if each seller has a positively sloped supply schedule?
2. Review of the revenue and cost curves of the firm and its long-run and short-run equilibrium. Comparative implications of competitive and monopolistic equilibrium.
   4. Show how the price elasticity of demand for a good is related to average and marginal revenue. Why is a monopolist never in static equilibrium in the range where his demand is relatively inelastic?
   5. Given the linear demand p = a –bq, show that price elasticity depends only on p and a, or only on q and a/b. When do two linear demands have the same elasticity (a) at any given price, (b) at any given quantity?
   6. Given two linear demand (with different slope and different axis-intercepts) and a point on one of them, find geometrically the point on the other with the same elasticity.
   7. A linear demand and a demand that is concave from above are tangent at a particular point. In the vicinity of that output, how much can you say about the relative magnitudes, slopes , and curvatures of the respective marginal revenue curves?
   8. Given relevant segments of a monopolist’s AR, MR, and MC curves (but not AC), show how much his profit is reduced if he is forced to charge a somewhat lower price than his profit-maximizing one—on the assumption that he still has an incentive to satisfy the full demand at the new price.
   9. “Short-run marginal cost is typically smaller than long-run marginal cost, since the former reflects only variable cost while the latter reflects full cost.” Discuss.
   10. Discuss the virtues and limitations of Lerner’s concept of the degree of monopoly power, M = (AR-MC)/AR. Would it make any difference if he had defined it as M´ = (AR-MR)/AR?
   11. “A profit-maximizing monopolist, in contrast to a pure competitor, would always prefer to sell more than he actually can, at the price he hooses to set. This is why monopolists frequently advertise and pure competitors never do; and it is also why equilibrium can be analyzed by means of demand and supply curves in pure competition but not in monopoly.” Discuss.

3. Long-run and short-run equilibrium of the purely competitive industry, with comparative statics problems. Supply curves reflecting pecuniary v. real or technological externalities.
   12. Give as many distinct reasons as you can why a purely competitive industry’s long-run supply curve may be positively sloped? Negatively sloped?
   13. “If a purely competitive industry’s long-run equilibrium is disturbed by a sudden increase in demand, the effects on price are likely to be greater in the short run than the long, and the effects on output are likely to be just the opposite.” Discuss.
   14. Under what circumstances, if any, is the Marshallian producers’-surplus area above a supply curve a defensible concept? When is it clearly indefensible?
   15. In a purely competitive industry with negatively sloped demand, can a commodity tax lower the price? Can it raise price by more than the amount of the tax? Show that the answers differ according as the stability conditions are assumed to be Walrasian or Marshallian.
   16. In a purely competitive industry where firms all have u-shaped costs and the industry’s long-run supply is horizontal, compare the effects of a specific commodity tax, a franchise tax, and a limited licensing of firms—such that all would have the same effect on industry output.
   17. Assume that a distinctive type of grape can be grown only on a distinctive type of vineyard land, which is valueless in any other use. This land varies widely in quality from one acre to another. The only other factor, labor, is homogeneous and in perfectly elastic supply to this single industry. (Assume, for convenience, that one firm always cultivates just one acre, irrespective of relative factor prices.)
       1. If the land is widely owned and the grape industry is purely competitive, show how its long-run supply curve is derived. Then, for some given grape demand, show how the aggregate equilibrium rent is determined.
       2. What would be the comparative effects of a tax on the grapes and a tax on the vineyard land that would raise the same revenue? Might the landlords ever prefer the latter tax?
       3. Starting from the equilibrium in (a), assume that laborers become free to allocate themselves on the vineyard land and receive equal per capita shares of the total grape revenue. How would this affect the price and quantity of grapes, incomes, and allocational efficiency?
   18. Explain why, in some purely competitive industries, social marginal cost may be different from private marginal cost.
4. Comparative statics of monopoly: changes of demand, cost, taxes, various regulations. Equilibrium with advertising, with price discrimination, with systematic seasonal shifts of demand.
   19. In a monopoly with negatively sloped demand, can a specific tax lower price? Can it raise price by more than the amount of the tax? Show that the answers depend on the second-order conditions for a profit maximum. Are these special results more or less likely than in pure competition (cf. question 15).
   20. For any given specific tax, does a fully equivalent ad valorem tax exist (a) in pure competition, (b) in monopoly?
   21. “Not only does a monopolized industry produce less than a competitive one would, but also when superior productive equipment becomes available, the monopolist is motivated to introduce it more slowly.” Explain wherein you agree or disagree.
   22. What determines whether a static-equilibrium monopoly price will rise or fall in response to an increase of demand? Does it make any difference whether the demand increase is spontaneous or induced by advertising? Can an increase in demand ever reduce a monopolist’s equilibrium output?
   23. Under what circumstances will a price ceiling imposed on a monopolist
       1. leave him with incentive to satisfy the full demand at that price,
       2. induce him to produce an output that is positive but not great enough to satisfy the full demand, or
       3. drive him out of business?
   24. “The greater is a firm’s degree of monopoly power (in Lerner’s sense), the more likely is it to find advertising profitable.” What can be said for and against this proposition?
   25. When is it profitable to discriminate as to price in two markets for a physically homogeneous product? Are there any circumstances in which the buyers in both markets may benefit from the discrimination?
5. Monopolistic competition: oligopoly and product differentiation.
   26. Why are none of the duopoly solutions proposed by Cournot, Bertrand, Stackelberg, and Chamberlin wholly satisfactory?
   27. If duopolists produce differentiated products, what are the comparative consequences under (a) price-quoting and (b) quantity-setting? Specifically, compare the Cournot and Bertrand equilibria, the corresponding Stackelberg equilibria (and warfares), the potentialities for collusion, and the potentialities for warfare.
   28. How and why is the problem of oligopolistic interdependence allegedly avoided in Chamberlin’s large-group case of monopolistic competition? Are you satisfied that it is really avoided? Compare it in this respect with pure competition.
   29. As compared with simple monopoly, what additional sources of uncertainty are there with respect to comparative-statics problems under monopolistic competition?

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Waiver Exam—14.122
September 11, 1974

Answer any TWO questions (about 40 minutes each):

Question 1:

1. Show how the total, average, and marginal cost curves of a one-product firm are related to one another in the long-run—as to intersections, minima, inflection points, etc. (Assume that the total-cost function is continuous up to at least its second derivative and that production is subject first to net economies of scale and then to net diseconomies.)
2. Show how those same long-run cost curves are related to their short-run counterparts, identifying all notable points of correspondence.

Question 2:

In a small community surrounding a lake, workers can get all the employment they need in industry at a wage of $20 per day. An alternative employment is to catch fish in the lake and sell it in the environs at a constant price of $10 per bushel. With labor valued at the going wage, the cost of fish per bushel rises with the total amount of fishing. Specifically, the average cost of fish (in dollars per bushel) is related thus to the total number of bushels caught per day:

C = 2 + .005q

1. With free entry to the lake, how much fish will be caught?
2. Show that everybody can be made better off if the community levies an appropriate tax per bushel of fish. What is the optimal tax?
3. If, alternatively, the lake were privately owned and the owner could hire labor to catch fish at the same cost as before, what output would maximize his net income?
4. Would it always be appropriate, as in (b), to impose a tax on any competitive industry with a positively sloped supply curve? Explain briefly.

Question 3:

“If a specific tax of given magnitude is imposed on a good that is producible at constant unit cost, the equilibrium price may be raised either more or less under monopoly than under competition. Even when the price rises by an appreciably smaller amount under monopoly, however, it is still very likely to be socially disadvantageous to tax such a monopolized good rather than competitive ones.” Explain fully wherein you agree or disagree with each sentence.

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14.122
November 1, 1974

One hour and a half
Answer any FIVE of the following six questions:

1. If a specific tax is imposed on a commodity produced by a purely competitive industry, what effects on price can be ruled out under the stability conditions specified by (a) Marshall; (b) Walras? Explain.
2. You are given this cost function:

C= aq_c + bq,

where C is total cost, q_c is an absolute-capacity output (fixed in the short run), q is the actual output (less than or equal to q_c), and a and b are positive constants. Draw carefully the implied long-run cost schedules and several sample sets of short-run cost schedules—total, average and marginal. Comment on the relationship between long-run and short-run marginal cost.

3. “When the demand for a monopolist’s product increases, his profit-maximizing price may rise, remain the same, or fall. The conditions governing this result are exactly the same whether the increase in demand is spontaneous or induced by advertising.” Explain why you agree or disagree.
4. “Fully equivalent specific and ad valorem taxes are possible in pure competition but not in monopoly.” Explain why you agree or disagree.
5. When does a positively sloped supply curve imply some form of producers’ surplus, and when does it not? Explain.
6. In an oligopoly with differentiated products, would the price be lower in a Cournot equilibrium or a Bertrand equilibrium? Explain.

Source: Personal copies.

Image Source:Robert L. Bishop at MIT Museum  .