Consider a firm that produces a single output good Y with two inputgoods: labor (L) and capital (K). The firm has a technology describedby the production function f : R? → R+ defined byf(1, k) = 21 + 5k, where l is the quantity of labor and k is the quantity of capital.Suppose that input prices are (w, r) >> 0, where w is the wage rate(price of a unit of labor) and r is the interest rate (price of a unit ofcapital), and p > 0 is the price of the output good Y.(a) Formulate the firm's profit maximization problem.(b) Under what conditions on the prices (w, r,p) is there a solution tothe profit maximization problem?(c) Under what conditions on the prices (w, r, p) is there a solutionto the profit maximization problem where the firm is willing tosupply a strictly positive quantity of output?(d) Suppose pwhat conditions does the firm use only labor to produce the output,= 1 and the firm supplies 100 units of output. Underand how much labor does the firm demand in that case?

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Answered: Consider a firm that produces a single…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R → R+ defined by f(1, k) = 21 + 5k,