Let Q = F(K, L) = K'*L'4 denoted a production function with K as capital input and L as labour input. The price per unit of output is p, the price per unit of capital is r, and the price per unit of labor is w.(a) Write down the profit function r.(b) Write down the first-order conditions for maximum profit.(c) Find the choices K* = K * (p, r, w) of K and L* = L* (p, r, w) of L that maximize 1.(d) Let t * (p, r, w) = T(K * , L*, p, r, w) be the optimal profit as a function of (p, r,w). Show that dn * / op = F(K* , L * ) = Q*. (Special case of Hotelling's lemma.)(a)Write down the profit function î.1(K, L, p, r, w) = (b)Write down the first-order conditions for maximum profit.11/4 -r = 0%3DdK- w = 0=(c)Find the choices K* = K* (p, r, w) of K and L * = L* (p, r, w) of L that maximize T.K* =-1/2w1L* =(d)Let î* (p, r, w) = (K * , L*, p, r, w) be the optimal profit as a function of (p, r, w). Show that of * / op = F(K * , L* ) = Q*. (Special case of Hotelling's lemma.)1Begin by finding Q * = (K * )'(L * )'/4 = -pr%3DW4Next computeî(K * , L *, p, r, w) = p(K * )'/(L * )"/4 - rK* - wL * =

Let Q = F(K, L) = KL* denoted a production function with K as capital input and L as labour input. The price per unit of output is p, the price per unit of capital is r, and the price per unit of labor is w. (a) Write down the profit function . (b) Write down the first-order conditions for maximum profit. (c) Find the choices K* = K* (p, r, w) of K and L* =L* (p, r, w) of L that maximize î. (d) Let 1* (p, r, w) = (K * , L*, p, r, w) be the optimal profit as function of (p, r,w). Show that dn* / dp = F(K *, L*) = Q*. (Special case of Hotelling's lemma.) (a) Write down the profit function . (K, L, p, r, w) =

Let Q = F(K, L) = KL* denoted a production function with K as capital input and L as labour input. The price per unit of output is p, the price per unit of capital is r, and the price per unit of labor is w. (a) Write down the profit function . (b) Write down the first-order conditions for maximum profit. (c) Find the choices K* = K* (p, r, w) of K and L* =L* (p, r, w) of L that maximize î. (d) Let 1* (p, r, w) = (K * , L, p, r, w) be the optimal profit as function of (p, r,w). Show that dn / dp = F(K , L) = Q*. (Special case of Hotelling's lemma.) (a) Write down the profit function . (K, L, p, r, w) =

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

Chapter9: Applications Of Cost Theory

Section: Chapter Questions

Problem 3E

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