Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. the prices of each unit of capital and labor are r and w, The output good y sells for $p per unit. Firm A’s production function is y = fA(K,L) = K1/4 L1/4. The profit function is thus: ðA(K,L) = K1/4 L1/4 – rK -wL Find the profit maximizing levels of K and L as functions of r, w, and p. Suppose that r = w = $1 and p = $4. What is the profit maximizing level of output, y ?

Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. the prices of each unit of capital and labor are r and w, The output good y sells for $p per unit. Firm A’s production function is y = fA(K,L) = K1/4 L1/4. The profit function is thus: ðA(K,L) = K1/4 L1/4 – rK -wL Find the profit maximizing levels of K and L as functions of r, w, and p. Suppose that r = w = $1 and p = $4. What is the profit maximizing level of output, y ?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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Consider two firms that produce a single output good,y, using two inputs :Capital, K , and labor, L, the prices of each unit of capital and labor are r and w,respectively. The output good y sells for $p per unit. Firm A's production function is y = fa(K,L) = K1/4L1/4. The profit function is equals to : K1/4L1/4 - rK -wL. a) FInd the profit maximizing levels of K and L as functions of r,w, and p. b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?
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