Consider a two-period monopoly facing the negatively sloped inverse demand function pt = p(qt) in each period t = 0,1. The firm maximizes the present discounted value of profits, PDV = E}=0(1+r)-'nt, where r > 0 is the market interest rate, and Tt is period-t profit. In each of the following, assume that costs each period are increasing in that period's output and a strictly convex, and that PDV is strictly concave. (a) If costs are C; = c(qt) for t = 0,1, show that the firm will "short-run profit maximize" in each period by choosing output to equate marginal cost and marginal revenue in each period. (b) Now suppose that the firm can "learn by doing". Its first period costs are simply co = co(q0). Its second period costs, however, depend on first period output; c = Does the firm still "short-run profit maximize" in each period? Why or why not? Interpret your c(41, 90), where dc1/@qo < 0. results.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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Consider a two-period monopoly facing the negatively sloped inverse demand function pt = p(qt) in each
period t = 0,1. The firm maximizes the present discounted value of profits, PDV = E:=0(1+r)-tnt,
where r > 0 is the market interest rate, and T is period-t profit. In each of the following, assume that
costs each period are increasing in that period's output and a strictly convex, and that PDV is strictly
concave.
(a) If costs are c; =
c(q:) for t = 0,1, show that the firm will "short-run profit maximize" in each
period by choosing output to equate marginal cost and marginal revenue in each period.
(b) Now suppose that the firm can "learn by doing". Its first period costs are simply Co = co(q0). Its
second period costs, however, depend on first period output; c = c(q1, 90), where dc/dq0 < 0.
Does the firm still "short-run profit maximize" in each period? Why or why not? Interpret your
results.
Transcribed Image Text:Consider a two-period monopoly facing the negatively sloped inverse demand function pt = p(qt) in each period t = 0,1. The firm maximizes the present discounted value of profits, PDV = E:=0(1+r)-tnt, where r > 0 is the market interest rate, and T is period-t profit. In each of the following, assume that costs each period are increasing in that period's output and a strictly convex, and that PDV is strictly concave. (a) If costs are c; = c(q:) for t = 0,1, show that the firm will "short-run profit maximize" in each period by choosing output to equate marginal cost and marginal revenue in each period. (b) Now suppose that the firm can "learn by doing". Its first period costs are simply Co = co(q0). Its second period costs, however, depend on first period output; c = c(q1, 90), where dc/dq0 < 0. Does the firm still "short-run profit maximize" in each period? Why or why not? Interpret your results.
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