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Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/IrwinManagerial Economics, 9e
Managerial Economics ThomasMauriceninth edition
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/IrwinManagerial Economics, 9e
Managerial Economics ThomasMauriceninth edition
Chapter 10
Production & Cost Estimation
Managerial EconomicsManagerial Economics
10-2
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
3 3 2 2Q aK L bK L
Managerial EconomicsManagerial Economics
10-3
Properties of a Short-Run Cubic Production Function
• Holding capital constant, short-run cubic production function is derived as follows:
3 2Q AL BL
3 3 2 2Q aK L bK L 3 2AL BL
3 2A aK B bKWhere and
Managerial EconomicsManagerial Economics
10-4
Properties of a Short-Run Cubic Production Function
• The average & marginal products of labor are, respectively:
3 2Q AL BL
2AP Q L AL BL
2MP Q L 3AL 2BL
Managerial EconomicsManagerial Economics
10-5
Properties of a Short-Run Cubic Production Function
• Marginal product of labor begins to diminish beyond Lm units of labor
3 2Q AL BL
aLAverage product of labor begins todiminish beyond units of labor•
m aB B
L L3A 2A
and
Managerial EconomicsManagerial Economics
10-6
MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1)
Q = AL3 + BL2
Managerial EconomicsManagerial Economics
10-7
Properties of a Short-Run Cubic Production Function
• To have necessary properties of a production function, parameters must satisfy the following restrictions:
3 2Q AL BL
A 0 B 0 and
Managerial EconomicsManagerial Economics
10-8
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
Managerial EconomicsManagerial Economics
10-9
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
Managerial EconomicsManagerial Economics
10-10
Properties of a Short-Run Cubic Cost Function
• Average variable cost & marginal cost functions are, respectively:
2 3TVC aQ bQ cQ
2AVC a bQ cQ
2SMC a 2bQ 3cQ
Managerial EconomicsManagerial Economics
10-11
Properties of a Short-Run Cubic Cost Function
• Average variable cost reaches its minimum value at:
2 3TVC aQ bQ cQ
mQ b 2c
0 0 0a , b , c and
• To conform to theoretical properties, parameters must satisfy the following restrictions:
Managerial EconomicsManagerial Economics
10-12
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
Managerial EconomicsManagerial Economics
10-13
Summary of Short-Run Empirical Production Functions
Short-run cubic production equations
Total product
Average product of labor
Marginal product of laborDiminishing marginal returns
Restrictions on parameters
3 2Q AL BL
2AP AL BL
23 2MP AL BL
0 0A Band
3m
BL
Abegin at
Managerial EconomicsManagerial Economics
10-14
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
2 3TVC aQ bQ cQ
2AVC a bQ cQ
22 3SMC a bQ cQ
2m
bQ
c
0 0 0a , b , c