Production functions Economists model the output of manufacturing systems using production functions that have many of the same properties as utility functions. The family of Cobb-Douglas production functions has the form P = ƒ(K, L) = CKa L1 - a, where K represents capital, L represents labor, and C and a are positive real numbers with 0 < a < 1. If the cost of capital is p dollars per unit, the cost of labor is q dollars per unit, and the total available budget is B, then the constraint takes the form pK + qL = B. Find the values of K and L that maximize the following production functions subject to the given constraint, assuming K ≥ 0 and L ≥ 0. P = ƒ(K, L) = 10K1/3 L2/3 for 30K + 60L = 360
Production functions Economists model the output of manufacturing systems using production functions that have many of the same properties as utility functions. The family of Cobb-Douglas production functions has the form P = ƒ(K, L) = CKa L1 - a, where K represents capital, L represents labor, and C and a are positive real numbers with 0 < a < 1. If the cost of capital is p dollars per unit, the cost of labor is q dollars per unit, and the total available budget is B, then the constraint takes the form pK + qL = B. Find the values of K and L that maximize the following production functions subject to the given constraint, assuming K ≥ 0 and L ≥ 0. P = ƒ(K, L) = 10K1/3 L2/3 for 30K + 60L = 360
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Production functions Economists model the output of manufacturing systems using production functions that have many of the same properties as utility functions. The family of Cobb-Douglas production functions has the form P = ƒ(K, L) = CKa L1 - a, where K represents capital, L represents labor, and C and a are positive real numbers with 0 < a < 1. If the cost of capital is p dollars per unit, the cost of labor is q dollars per unit, and the total available budget is B, then the constraint takes the form pK + qL = B. Find the values of K and L that maximize the following production functions subject to the given constraint, assuming K ≥ 0 and L ≥ 0.
P = ƒ(K, L) = 10K1/3 L2/3 for 30K + 60L = 360
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