Consider a competitive firm which uses three inputs K (capital), L (labor), and A (land) to produce output y. The input prices are (WK = 2; WL = 1; WA = 4) and theoutput price is p = 1. The firm has the following production function: f (K, L, A) = A (√L+√K). In the short run, the firm's land level is fixed at A, but can choose labor and capital as it wishes. In the long run, the firm can also vary its land level. (a) Derive the short-run cost function given Ā. (b) Use the short-run cost function to derive the long-run cost function. [Hint: Use an approach, where the profit-maximization problem can be decomposed into two steps. Here try to decompose the long-run cost minimization problem into two steps
Consider a competitive firm which uses three inputs K (capital), L (labor), and A (land) to produce output y. The input prices are (WK = 2; WL = 1; WA = 4) and theoutput price is p = 1. The firm has the following production function: f (K, L, A) = A (√L+√K). In the short run, the firm's land level is fixed at A, but can choose labor and capital as it wishes. In the long run, the firm can also vary its land level. (a) Derive the short-run cost function given Ā. (b) Use the short-run cost function to derive the long-run cost function. [Hint: Use an approach, where the profit-maximization problem can be decomposed into two steps. Here try to decompose the long-run cost minimization problem into two steps
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.6P
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Transcribed Image Text:Consider a competitive firm which uses three inputs K (capital), L
(labor), and A (land) to produce output y. The input prices are (WK = 2;
WL = 1; WA = 4) and theoutput price is p = 1. The firm has the following
production function: f (K, L, A) = A (√L+√K).
In the short run, the firm's land level is fixed at A, but can choose
labor and capital as it wishes. In the long run, the firm can also vary
its land level.
(a) Derive the short-run cost function given Ā.
(b) Use the short-run cost function to derive the long-run cost
function. [Hint: Use an approach, where the profit-maximization
problem can be decomposed into two steps. Here try to decompose
the long-run cost minimization problem into two steps
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