Managerial Economics ninth edition Thomas Maurice Chapter 10

Managerial Economics ninth edition Thomas Maurice Chapter 10 Production & Cost Estimation Mc. Graw-Hill/Irwin Managerial Economics, 9 e Copyright © 2008 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Managerial Economics 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 2

Managerial Economics Properties of a Short-Run Cubic Production Function • Holding capital constant, short-run cubic production function is derived as follows: 3

Managerial Economics Properties of a Short-Run Cubic Production Function • The average & marginal products of labor are, respectively: 4

Managerial Economics Properties of a Short-Run Cubic Production Function • Marginal product of labor begins to diminish beyond Lm units of labor • 5

Managerial Economics MP & AP Curves for the Short-Run Cubic Production Function (Figure 10. 1) Q = AL 3 + BL 2 6

Managerial Economics Properties of a Short-Run Cubic Production Function • To have necessary properties of a production function, parameters must satisfy the following restrictions: 7

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 = L 3 and W = L 2 • Estimated regression line must pass through the origin • Specify in computer routine 8

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 do 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 9

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

Managerial Economics Properties of a Short-Run Cubic Cost Function • Average variable cost reaches its minimum value at: • To conform to theoretical properties, parameters must satisfy the following restrictions: 11

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 • Not explicitly included in cost equation 12

Managerial Economics 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 13

Managerial Economics 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 14