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Managerial Economics: Applications, Strategy and Tactics 12th Edition by James McGuigan, Charles Moyer, Frederick Harris
Edition 12ISBN: 9781439079232Managerial Economics: Applications, Strategy and Tactics 12th Edition by James McGuigan, Charles Moyer, Frederick Harris
Edition 12ISBN: 9781439079232 Exercise 10
Extension of the Cobb-Douglas Production Function-The Cobb-Douglas production function (Equation) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: 11
![Extension of the Cobb-Douglas Production Function-The Cobb-Douglas production function (Equation) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: 11 where is an efficiency parameter that shows the output resulting from given quantities of inputs; is a distribution parameter (0 1) that indicates the division of factor income between capital and labor; is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and is a scale parameter ( 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Show that when = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of , or K* = ( )K and L* = ( )L, and show that output Q also increases by a factor of , or Q* = ( )(Q).] Equation 11 See R. G. Chambers, Applied Production Analysis (Cambridge: Cambridge University Press, 1988).](https://storage.examlex.com/SM2930/11eb693f_faa2_c7fd_a8d9_57dc1fa0a6e9_SM2930_11.jpg)
where is an efficiency parameter that shows the output resulting from given quantities of inputs; is a distribution parameter (0 1) that indicates the division of factor income between capital and labor; is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and is a scale parameter ( 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Show that when = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of , or K* = ( )K and L* = ( )L, and show that output Q also increases by a factor of , or Q* = ( )(Q).]
Equation
![Extension of the Cobb-Douglas Production Function-The Cobb-Douglas production function (Equation) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: 11 where is an efficiency parameter that shows the output resulting from given quantities of inputs; is a distribution parameter (0 1) that indicates the division of factor income between capital and labor; is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and is a scale parameter ( 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Show that when = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of , or K* = ( )K and L* = ( )L, and show that output Q also increases by a factor of , or Q* = ( )(Q).] Equation 11 See R. G. Chambers, Applied Production Analysis (Cambridge: Cambridge University Press, 1988).](https://storage.examlex.com/SM2930/11eb693f_faa2_ef0e_a8d9_3b8d9fc09867_SM2930_00.jpg)
11 See R. G. Chambers, Applied Production Analysis (Cambridge: Cambridge University Press, 1988).
where is an efficiency parameter that shows the output resulting from given quantities of inputs; is a distribution parameter (0 1) that indicates the division of factor income between capital and labor; is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and is a scale parameter ( 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Show that when = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of , or K* = ( )K and L* = ( )L, and show that output Q also increases by a factor of , or Q* = ( )(Q).]
Equation
11 See R. G. Chambers, Applied Production Analysis (Cambridge: Cambridge University Press, 1988).
Explanation
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Verified
According to the information given in th...
Managerial Economics: Applications, Strategy and Tactics 12th Edition by James McGuigan, Charles Moyer, Frederick Harris
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