A: Now consider the same set-up as in exercise 13.7 but assume throughout that labor is instantaneously variable, that capital is fixed in the short run and variable in the intermediate run, and that the choice of technology is fixed in the short and intermediate run but variable in the long run.

(a) Suppose you are currently long-run profit maximizing. Graph the (long run) supply curve you derived in part A(i) of exercise 13.7 and indicate a price p and quantity x combination that is consistent with using the non-patented technology.

(b) Next suppose that output price increases to P̅ and that this increase is sufficient for you to wish that you in fact had rented the patented technology instead. Illustrate how your output level will adjust in the intermediate run to x^IR.

(c) In the short run, your firm cannot change its level of capital. Where would your short run optimal output level x^SR (at the new P̅) lie relative to x and x^IR? How is your answer impacted by the relative substitutability of capital and labor in the non-patented technology?

(d) In the long run, where will your optimal output level x^LR lie?

(e) Suppose price had fallen to P̅ instead of rising to P̅. Indicate where your short, intermediate and long run output levels would lie.

(f) On a new graph, illustrate the short, intermediate and long run supply curves for your firm given you started at the original price p and the original optimal output level x.

(g) What would your last graph look like if you had originally started at price P̅ and had originally produced at the long run optimal output level x^LR?

B: Suppose, as in exercise 13.7, that the two technologies available to you can be represented by the production functions f (ℓ,k) = 19.125ℓ^0.4 k^0.4 and g (ℓ,k) = 30ℓ0^.2k^0.6, but technology g carries with it a recurring fee of F. Suppose further that w = 20, r = 10 and F = 1,000.

(a) If p = 2.25 and the firm is currently long run optimizing, how much does it produce? (You can use what you learned from exercise 13.7 and employ equation (13.49).)

(b) Now suppose the output price increases from 2.25 to 2.75. How much will the firm adjust output in the short run (where neither capital nor technology can be changed)?³

(c) How much will it increase output in the intermediate run (where capital can adjust but technology remains fixed)?

(d) How much will it adjust output in the long run?

(e) What happens to the quantity of labor and capital hired in the short, intermediate and long run?

(f) Suppose that instead of increasing, the output price had fallen from 2.25 to 2.00. What would have happened to output in the short, intermediate and long run?

(g) Suppose that the firm has fully adjusted to the higher output price of 2.75. Then price falls to 2.25. What happens to output in the short, intermediate and long run?

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