Carnegie Tech. Final Exam for Advanced Economic Analysis. Modigliani, 1959 & 1960

An earlier post provided the outline for Franco Modigliani’s Advanced Economic Analysis course from the second term of the 1958-59 academic year that had been incorrectly filed in a folder of his notes for Advanced Monetary Theory III, 1953-1960″. A copy of the June 3, 1959 final examination was provided to Economics in the Rear-view Mirror for transcription by Juan Acosta.  I have added the May 27, 1960 final examination to this post as a second observation.

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June 3, 1959

Advanced Economic Analysis I – GI 581
Final Examination

Answer questions I and IV, and either II or III.

1. Assume that the government fixes by law the price of a commodity and hands out to the public ration coupons equal in number to the number of units of the commodity produced. Assume throughout that the supply is perfectly inelastic.
   1. Use an indifference diagram to show under what conditions the consumer would not use all of his coupons.
   2. Show that consumers would be better off if they were free to buy or sell their ration coupons in a free market.
   3. Supposing now that coupons could be bought and sold in a free market, explain how one could derive an individual consumer’s demand curve for coupons. (Hint: the situation is analogous to the consumer being forced to buy his ration of the good at the legal price and then being allowed to sell it or buy more of it on a free market.)
   4. Explain the formation of the equilibrium market price of coupons.
   5. What can be said as to the relation between the legal price, the price of coupons, and the price which would prevail in the absence of price control and rationing? Under what condition would the sum of the first two be equal to the third?
2. A producer sells in his home market, in which he has a monopoly, and in a foreign market which is perfectly competitive. How would a sales tax imposed on the home market affect
   1. total output
   2. price in the home market
   3. price in the foreign market
   4. distribution of output between the two markets
3. A profit maximizing monopolist buys factors of production in a perfect market.
   1. Discuss the long-run effect on his demand for each of the factors he uses and on his selling price of a tax on one of the factors. (Give a graphic treatment for the case of two factors.)
   2. Suppose that one of the two factors is fixed in the short run. Contrast the change in the long-run and short-run demand for both factors when a tax is placed on either.
4. Discuss the significance of free entry for the relation of the long-run equilibrium size of the firm to the optimum size.

 

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library. Economists’ Papers Archive. Franco Modigliani Papers, Box T1, Folder “Advanced Economics,1952-1960”.

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May 27, 1960

GI-581 Advanced Economic Analysis I
Final Examination
F. Modigliani

 

1. (Answer questions a-f; question g is elective)
   Suppose that the conditions of production for a given firm can be expressed by the production function.
   (1) X = KA^aB^b
   where A and B represent the inputs of two factors, X the output, and K, a, b, certain constants.
   1. Explain the meaning of a production function.
   2. Given the prices, P_A, and P_B of the two inputs determine the optimum input of each factor as a function of X, P_A, P_B.
   3. Exhibit the (minimized) total and marginal cost functions.
   4. Under what conditions is the above marginal cost increasing, decreasing or constant? Relate this result to the degree homogeneity of the production function (1) and to the notion of returns to scale.
   5. Discuss the relation between returns to scale and returns to each factor separately.
   6. How would you obtain the demand function of the firm for each factor, (i) if the firm sells in a competitive market? (ii) if the firm has a monopoly in the selling market?
   7. (Elective)
      Suppose that equation (1) describes the conditions of production for an entire industry, and assume further that the supply of factor A is infinitely elastic at the price P_A while the conditions of supply of factor B can be expressed by the supply function P_B = LB^s, when L and s are constants, (s>0).
      1. The industry is composed of a large number of firms each of which takes the prices of the factors as given and independent of its inputs decisions;
      2. The entire industry is monopolized.
         Obtain the marginal cost for the industry in each of these two cases. What is the relation between this marginal cost and the supply functions? How is the slope of the supply function related to notion of returns to scale and of external and internal economies or diseconomies?
2. In the figure below, X and Y denote the quantities of two commodities. Shown in the graph are four budget equations and the points chosen on each by a consumer.
   1. State the revealed preference postulate.
   2. Using this postulate, rank as far as possible the four points in order of preference.
   3. Draw a fifth budget line and observed point on it which would make possible an unambiguous ranking of the original four points.
   4. (Optional) Sketch out how the revealed preference postulate can be used to establish the slope of the Marshallian Demand function.

3. Discuss briefly the meaning and significance of the following concepts and their interrelation in Economics:
   1. Statics;
   2. Dynamics;
   3. Comparative statics;
   4. Long and short run
      Discuss the notion of “long run,” “short run” and “reversibility” as they apply to demand functions.

 

Source: Duke University. David M. Rubenstein Rare Book & Manuscript Library. Economists’ Papers Archive. Franco Modigliani Papers, Box T8, Folder “Notes on Advanced Monetary Theory III,1953-1960”.

Image Source: Franco Modigliani page at the History of Economic Thought Website.