Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s productionfunction is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P perunit, and the owner’s time costs $1 per unit.a. Write down Needful Things’ profit function.b. Suppose in the short run, the owner’s time is fixed at T=16. Find the first order condition for the short-runprofit maximizing amount of labor.c. Solve for the amount of labor that the shop uses in the short run to maximize profit as a function of P. Is youranswer consistent with the law of demand? Explain. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizingamounts of both inputs. e. Solve for the amount of labor and time that Needful Things uses to maximize profit in the long run.

Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s productionfunction is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P perunit, and the owner’s time costs $1 per unit.a. Write down Needful Things’ profit function.b. Suppose in the short run, the owner’s time is fixed at T=16. Find the first order condition for the short-runprofit maximizing amount of labor.c. Solve for the amount of labor that the shop uses in the short run to maximize profit as a function of P. Is youranswer consistent with the law of demand? Explain. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizingamounts of both inputs. e. Solve for the amount of labor and time that Needful Things uses to maximize profit in the long run.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section: Chapter Questions

Problem 17QP

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Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s production function is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P per unit, and the owner’s time costs $1 per unit. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizing amounts of both inputs. e. Solve for the amount of labor and time that Needful Things uses to maximize profit in the long run.
Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners’ time (T). The shop’s production function is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P per unit, and the owner’s time costs $1 per unit. d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizing amounts of both inputs.
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