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Suppose that George operates a laundromat which requires two inputs, capital (K) and labor (L). His production function is Q=3K^(1/3)*L^(1/3).

a) Suppose George desires to produce 90 units of output, and the cost of labor is $27. What is the capital demand curve?

b) Suppose George desires to produce 90 units of output, the cost of capital is $1 and the cost of labor is $27. What is his price elasticity of capital demand? Comment.

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 workers. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225?

A price taking firm chooses its inputs to maximize short-run profits. Its Cobb-Douglass production function has the following form: q(L, K) = L^(1/2) K ^(1/3) . The output price is 1,000 per unit and the cost of each unit of input is 10. In the short-run, capital is fixed at 27 units.

(a) Set up the profit function in terms of labor only.

(b) Find the optimal choice of labor, L ∗ .

(c) Given your answer to part (b), do you think that there is excess capital compared to the optimal level of quantity?

Another price taking firm chooses its inputs to maximize long-run profits. Labor and capital are substitutes in production and both exhibit decreasing returns to scale, q(L, K) = L^(1/2) + K^(1/2) . The output price is 100 and the price of each of the inputs is 10.

(a) Set up the firm’s profit function and provide the two conditions for profit maximization.

(b) Find the profit maximizing levels of capital and labor.

(c) How does a change in labor change the optimal choice of capital?

A manufacturing firm's production function is Q = KL + K + L. The price r of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing firm use

a) only labor?

b) only capital?

c) both labor and capital?

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