Chapter 10 - Production and cost estimation. 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,...
Managerial Economics ninth edition Thomas Maurice Chapter 10 Production & Cost Estimation McGrawưHill/Irwin McGrawưHill/Irwin ManagerialEconomics,9e ManagerialEconomics,9e Copyrightâ2008bytheMcGrawưHillCompanies,Inc.Allrightsreserved ManagerialEconomics 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 Q 102 3 aK L 2 bK L Managerial Economics Properties of a Short-Run Cubic Production Function Q AL BL • Holding capital constant, short-run cubic production function is derived as follows: Q 2 aK L bK L AL BL W h e r e A 103 aK and B bK Managerial Economics Properties of a Short-Run Cubic Production Function Q AL BL • The average & marginal products of labor are, respectively: AP MP 104 Q L Q L AL BL AL 2BL Managerial Economics Properties of a Short-Run Cubic Production Function Q AL BL • Marginal product of labor begins to diminish beyond Lm units of labor • Average product of labor begins to diminish beyond La units of labor Lm 105 B and La 3A B 2A Managerial Economics MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1) Q = AL3 + BL2 106 Managerial Economics Properties of a Short-Run Cubic Production Function Q AL BL • To have necessary properties of a production function, parameters must satisfy the following restrictions: A and B 107 Managerial Economics 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 108 Managerial Economics Estimation of a Short-Run Cost Function • Estimate using data for which the level of usage of one or more inputs is fixed • Usually time series data are used • Data collection may be complicated by the fact that accounting data not include firm’s opportunity costs • Capital costs should reflect not only acquisition cost but any foregone rental income, depreciation, & capital gains/losses • Must eliminate effects of inflation • Divide by appropriate price index 109 Managerial Economics Properties of a Short-Run Cubic Cost Function TVC aQ bQ cQ • Average variable cost & marginal cost functions are, respectively: a bQ cQ AVC SMC 10 a 2bQ 3cQ Managerial Economics Properties of a Short-Run Cubic Cost Function TVC aQ bQ cQ • Average variable cost reaches its minimum value at: Qm b 2c • To conform to theoretical properties, parameters must satisfy the following restrictions: a 10 0, b , and c Managerial Economics Properties of a Short-Run Cost Function • Cubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curves • 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 10 • Not explicitly included in cost equation Managerial Economics Summary of Short-Run Empirical Production Functions Short-run cubic production equations Average product of labor Marginal product of labor Diminishing marginal returns Restrictions on parameters 10 AL3 Q Total product AP MP BL2 AL BL AL2 BL b e g in at Lm A and B B 3A Managerial Economics Summary of Short-Run Empirical Cost Functions Short-run cubic cost equations Total variable cost Average variable cost Marginal cost SMC 10 a Qm a cQ a bQ cQ AVC Average variable cost reaches minimum at Restrictions on parameters aQ bQ TVC 0, b 2bQ 3cQ b 2c 0, c ... units of labor Lm 10 5 B and La 3A B 2A Managerial Economics MP & AP Curves for the Short-Run Cubic Production Function (Figure 10. 1) Q = AL3 + BL2 10 6 Managerial Economics Properties... Divide by appropriate price index 10 9 Managerial Economics Properties of a Short-Run Cubic Cost Function TVC aQ bQ cQ • Average variable cost & marginal cost functions are, respectively: a bQ cQ AVC SMC 10 a 2bQ 3cQ Managerial Economics. .. h e r e A 10 3 aK and B bK Managerial Economics Properties of a Short-Run Cubic Production Function Q AL BL • The average & marginal products of labor are, respectively: AP MP 10 4 Q L Q