10. Extension of the Cobb-Douglas Production Function–The Cobb-Douglas produc- tion function (Equation 7.16) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form:" Q = ylƏK*° + (1 – a)L"®]W/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; a is a distribution parameter (0 sas 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 pro- duction process; and v is a scale parameter (v > 0) that indicates the type of re- turns to scale (increasing, constant, or decreasing). Show that when v = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of A, or K* = (A)K and L* = (A)L, and show that output Q also increases by a factor of A, or Q* = (A)(Q).]

10. Extension of the Cobb-Douglas Production Function–The Cobb-Douglas produc- tion function (Equation 7.16) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form:" Q = ylƏK° + (1 – a)L"®]W/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; a is a distribution parameter (0 sas 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 pro- duction process; and v is a scale parameter (v > 0) that indicates the type of re- turns to scale (increasing, constant, or decreasing). Show that when v = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of A, or K = (A)K and L* = (A)L, and show that output Q also increases by a factor of A, or 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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