e Cobb-Douglas

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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Problem 5
The Cobb-Douglas production function with output Q and capital and labor inputs K and L, respectively,
is given by:
Q = f(K,L) = KªL®
where 0 < a <1 and 0 <B < 1.
Find the marginal product of capital fx(K,L) and marginal product of labor f.(K, L). Is production
increasing or decreasing with respect to capital? How about labor? (10 points)
b. Determine if the marginal product functions fx(K, L) and f.(K,L) are convex or concave. Give an
economic intuition to your answer. (10 points)
Transcribed Image Text:Problem 5 The Cobb-Douglas production function with output Q and capital and labor inputs K and L, respectively, is given by: Q = f(K,L) = KªL® where 0 < a <1 and 0 <B < 1. Find the marginal product of capital fx(K,L) and marginal product of labor f.(K, L). Is production increasing or decreasing with respect to capital? How about labor? (10 points) b. Determine if the marginal product functions fx(K, L) and f.(K,L) are convex or concave. Give an economic intuition to your answer. (10 points)
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