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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

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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
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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