In this chapter, you will learn to: Specify and estimate a short-run production function using a cubic specification of the production function, specify and estimate a short-run cost function using a cubic specification, estimate the parameters of a cubic short-run production function by using the technique of regression through the origin,. | Chapter 10: Production and Cost Estimation McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Empirical Production Function An empirical production function is the mathematical form of the production function to be estimated Empirical Production Function Long-run production function A production function in which all inputs are variable Short-run production function A production function in which at least one input is fixed Empirical Production Function Cubic empirical specification for a short-run production function is derived from a long-run cubic production function Cubic form of the long-run production function is expressed as Properties of a Short-Run Cubic Production Function Holding capital constant, short-run cubic production function is derived as follows: The average & marginal products of labor are, respectively: Properties of a Short-Run Cubic Production Function Marginal product of labor begins to diminish . | Chapter 10: Production and Cost Estimation McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Empirical Production Function An empirical production function is the mathematical form of the production function to be estimated Empirical Production Function Long-run production function A production function in which all inputs are variable Short-run production function A production function in which at least one input is fixed Empirical Production Function Cubic empirical specification for a short-run production function is derived from a long-run cubic production function Cubic form of the long-run production function is expressed as Properties of a Short-Run Cubic Production Function Holding capital constant, short-run cubic production function is derived as follows: The average & marginal products of labor are, respectively: Properties of a Short-Run Cubic Production Function Marginal product of labor begins to diminish beyond Lm units of labor Average product of labor begins to diminish beyond La units of labor Properties of a Short-Run Cubic Production Function MP & AP Curves for the Short-Run Cubic Production Function (Figure ) Q = AL3 + BL2 To have necessary properties of a production function, parameters must satisfy the following restrictions: A 0 Properties of a Short-Run Cubic Production Function Estimation of a Short-Run Production Function To use linear regression analysis, the cubic equation must be transformed into linear form Q = AX + BW Where X = L3 and W = L2 Estimated regression line must pass through the origin Specify in computer routine Estimate using data for which the level of usage of one or more inputs is fixed Usually time series data are used Estimation of a Short-Run Production Function Data collection may be complicated by the fact that accounting data do not include firm’s opportunity costs Capital costs should reflect not only acquisition .
