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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,

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,

MATLAB: An Introduction with Applications
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,
Transcribed Image Text: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,
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 of capital), 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 to the profit maximization problem? (c) Under what conditions on the prices (w, r, p) is there a solution to the profit maximization problem where the firm is willing to supply a strictly positive quantity of output? (d) Suppose p what conditions does the firm use only labor to produce the output, = 1 and the firm supplies 100 units of output. Under and how much labor does the firm demand in that case?
Transcribed Image Text: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 of capital), 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 to the profit maximization problem? (c) Under what conditions on the prices (w, r, p) is there a solution to the profit maximization problem where the firm is willing to supply a strictly positive quantity of output? (d) Suppose p what conditions does the firm use only labor to produce the output, = 1 and the firm supplies 100 units of output. Under and how much labor does the firm demand in that case?
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