**Cobb-Douglas Production Function and Returns to Scale**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:\[ Q = \gamma [\delta K^{-\rho} + (1 - \delta)L^{-\rho}]^{-\nu / \rho} \]where \( \gamma \) is an efficiency parameter that shows the output resulting from given quantities of inputs; \( \delta \) is a distribution parameter \( (0 \leq \delta \leq 1) \) that indicates the division of factor income between capital and labor; \( \rho \) is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and \( \nu \) is a scale parameter \( (\nu > 0) \) that indicates the type of returns to scale (increasing, constant, or decreasing).**Objective:**Complete the following derivation to show that when \( \nu = 1 \), this function exhibits constant returns to scale.**Derivation:**First of all, if \( \nu = 1 \):\[Q = \gamma [\delta K^{-\rho} + (1 - \delta)L^{-\rho}]^{-1 / \rho}\]\[= \gamma [\delta K^{-\rho (1/\rho)} + (1 - \delta)L^{-\rho (1/ \rho)}]\]\[= \gamma [\delta K^{-1} + (1 - \delta)L^{-1}]\]Then, increase the capital \( K \) and labor \( L \) each by a factor of \( \lambda \), or \( K^* = (\lambda)K \) and \( L^* = (\lambda)L \). If the function exhibits constant returns to scale, then \( Q^* = (\lambda)Q \).\[Q^* = \gamma [\delta (\lambda)K^{-1} + (1 - \delta)(\lambda)L^{-1}]\]\[= \gamma [\delta(\lambda^{-1/\rho}) + (1-\delta)\lambda^{-1/\rho}]\]\[= \gamma (\lambda^{-1/\rho}) [\delta K^{-1/\rho} + (1-\delta)L^{-

Where Y is an Efficiency Parameter ∂ is Distribution Parameter P is the Substitution Parameter

lowing mathematical form: Q=y[SK+ (1-8)L-P]-V/P here y is an efficiency parameter that shows the output resulting from given quantities of inputs; ō is a distribution parameter (0 ≤ 6 ≤ 1) that dicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor 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 creasing). mplete the following derivation to show that when v= 1, this function exhibits constant returns to scale. st of all, if v 1: = Y/SK P + (1-6)L-P]-1/P = Y/SK-P(-1/P) + (1-8)L-P(-1/P)] en, increase the capital K and labor L each by a factor of A, or K* = (A)K and L = (A)L. If the function exhibits constant returns to scale, then Q* = Q. * = y[5(A)K¯² + (1 - 5)(X)L¯P]-¹/P = y[SAK-P(-1/P) + (1 - 8)AL¯P(-1/P)] = AQ