The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=y[SKP + (1-8)L-P]-V/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; ō is a distribution parameter (0 ≤ ≤ 1) that indicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and v is a scale parameter (v> 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when v = 1, this function exhibits constant returns to scale. First of all, if v = 1: Q = = Y[SK-P+ (1-6)L-P]-1/P Y[SK-P(-1/P) + (1-6)L-P(-1/P)] Then, increase the capital K and labor L each by a factor of X, or K* = (A)K and L* = (A)L. If the function exhibits constant returns to scale, then Q* = (A)Q.

The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=y[SKP + (1-8)L-P]-V/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; ō is a distribution parameter (0 ≤ ≤ 1) that indicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and v is a scale parameter (v> 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when v = 1, this function exhibits constant returns to scale. First of all, if v = 1: Q = = Y[SK-P+ (1-6)L-P]-1/P Y[SK-P(-1/P) + (1-6)L-P(-1/P)] Then, increase the capital K and labor L each by a factor of X, or K* = (A)K and L* = (A)L. If the function exhibits constant returns to scale, then Q* = (A)Q.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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