McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 10 Production and Cost Estimation

10-2 Learning Objectives  Specify and explain the properties of a short ‐ run cubic production function  Employ regression analysis to estimate a short ‐ run production function  Discuss two important problems concerning the proper measurement of cost: correcting for inflation and measuring economic (opportunity) costs  Specify and estimate a short ‐ run cost function using a cubic specification

10-3 Empirical Production Function  An empirical production function is the mathematical form of the production function to be estimated

10-4 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

10-5 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

10-6 Properties of a Short-Run Cubic Production Function  Holding capital constant, short-run cubic production function is derived as follows:

10-7  The average & marginal products of labor are, respectively: Properties of a Short-Run Cubic Production Function

10-8  Marginal product of labor begins to diminish beyond L m units of labor  Average product of labor begins to diminish beyond L a units of labor Properties of a Short-Run Cubic Production Function

10-9 MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1) Q = AL 3 + BL 2

10-10  To have necessary properties of a production function, parameters must satisfy the following restrictions: A 0 Properties of a Short-Run Cubic Production Function

10-11 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 = L 3 and W = L 2  Estimated regression line must pass through the origin ~Specify in computer routine

10-12  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

10-13  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 cost but any foregone rental income, depreciation, & capital gains/losses Estimation of a Short-Run Production Function

10-14  Nominal cost data ~Data that have not been corrected for the effects of inflation  Must eliminate effects of inflation ~Correct for the influence of inflation by dividing nominal cost data by an appropriate price index (or implicit price deflator) Estimation of a Short-Run Production Function

10-15  Average variable cost & marginal cost functions are, respectively: Properties of a Short-Run Cubic Cost Function

10-16  Average variable cost reaches its minimum value at: Properties of a Short-Run Cubic Cost Function

10-17  To conform to theoretical properties, parameters must satisfy the following restrictions: a > 0, b 0 Properties of a Short-Run Cubic Cost Function

10-18  Cubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curves Properties of a Short-Run Cubic Cost Function

10-19  All three cost curves employ the same parameters ~Only necessary to estimate one of these functions to obtain estimates of all three  In the short-run cubic specification, input prices are assumed constant ~Not explicitly included in cost equation Properties of a Short-Run Cubic Cost Function

10-20 Summary of Short-Run Empirical Production Functions Short-run cubic production equations Total product Average product of labor Marginal product of labor Diminishing marginal returns Restrictions on parameters A 0

10-21 Summary of Short-Run Empirical Cost Functions Short-run cubic cost equations Total variable cost Average variable cost Marginal cost Average variable cost reaches minimum at Restrictions on parameters a > 0, b 0

10-22 Summary  The first step in estimating a production function is to specify the empirical production function, which is the exact mathematical form of the equation to be estimated  To estimate a cubic short-run production function using linear regression, transform the cubic equation into linear form; the estimated regression line must pass through the origin  A manager typically uses time-series observations on cost, output, and input prices to estimate the short-run cost function. The effects of inflation must be eliminated  Because all 3 cost curves ( TVC, AVC, and SMC ) employ the same parameters, one can estimate any one of them to obtain estimates of all 3 curves