|
|
|
|
|
|
|
|
|
|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
|
|
Egwald Economics: Microeconomics Production Functions
Egwald's popular web pages are provided without cost to users. Cobb-Douglas | CES | Generalized CES | Translog | Diewert | Translog vs Diewert | Diewert vs Translog | Estimate Translog | Estimate Diewert | References and Links With the Cobb-Douglas and CES production functions, I obtained an explicit cost function, total cost as a function of q, wL, wK, and wM, by minimizing the cost of producing a given level of output. Because the Translog production function is much more general (it has a flexible functional form permitting the partial elasticities of substitution between inputs to vary), I will use numerical analysis to obtain the cost functions associated with a given Translog production function. C. Translog (Transcendental Logarithmic) Production Function The three factor Translog production function is:
ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M) + bLL*ln(L)*ln(L) + bKK*ln(K)*ln(K) + bMM*ln(M)*ln(M) where L = labour, K = capital, M = materials and supplies, and q = product. I. To obtain estimates of the Translog production function, let us use the CES production function to generate a sequence of observations relating the CES least cost factor inputs to factor prices and levels of output. The three factor CES production function is: q = A * [alpha * (L^-rho) + beta * (K^-rho) + gamma *(M^-rho)]^(-nu/rho) where L = labour, K = capital, M = materials and supplies, and q = product. The parameter nu is a measure of the economies of scale, while the parameter rho yields the elasticity of substitution: sigma = 1/(1 + rho). The estimated coefficients of the Translog production and cost functions will vary with the parameters sigma, nu, alpha, beta and gamma of the CES production function. Set the parameters below to re-run with your own CES parameters.
Restrictions: .7 < nu < 1.3; .5 < sigma < 2; |
|