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Transcript of Chapter 10 Chapter 10Chapter 10Chapter 10Chapter 10Chapter 10
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8/19/2019 Chapter 10 Chapter 10Chapter 10Chapter 10Chapter 10Chapter 10
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8/19/2019 Chapter 10 Chapter 10Chapter 10Chapter 10Chapter 10Chapter 10
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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
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Managerial EconomicsManagerial Economics
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Properties of a Short-Run Cubic
Production Function
• Holding capital constant, short-run
cubic production function isderived as follows:
= +3 2Q AL BL
= +3 3 2 2
Q aK L bK L
= +3 2 AL BL
= =3 2 A aK B bK Where and
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Properties of a Short-Run Cubic
Production Function
• The average & marginal products
of labor are, respectively:
= +3 2Q AL BL
= = +2
AP Q L AL BL
= ∆ ∆ = +2 MP Q L 3AL 2BL
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Managerial EconomicsManagerial Economics
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Properties of a Short-Run Cubic
Production Function
• Marginal product of labor begins to
diminish beyond Lm units of labor
= +3 2Q AL BL
a L
verage product of labor begins to
diminish beyond units of labor
•
= − = −m a
B B L L
3 A 2 A and
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Managerial EconomicsManagerial Economics
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MP & AP Cures for the Short-Run
Cubic Production Function !Figure 10"1#
% & A'( )*'2
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Properties of a Short-Run Cubic
Production Function
• To have necessary properties of a
production function, parametersmust satisfy the following
restrictions:
= +3 2Q AL BL
< > A 0 B 0and
ll
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Estimation of a Short-Run
Production Function• To use linear regression analysis, thecubic e!uation must be transformed
into linear form
• Q = AX + BW
• Where X = L3 and W = L2
• "stimated regression line must pass
through the origin
• Specify in computer routine
M i l E iM i l E i
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Estimation of a Short-Run Cost
Function• "stimate using data for which the level ofusage of one or more inputs is fixed
• Usually time series data are used
•#ata collection may be complicated by thefact that accounting data do not include
firm$s opportunity costs
• Capital costs should reflect not only acquisition
cost but any foregone rental income,depreciation, & capital gains/losses
• Must eliminate effects of inflation
• Divide by appropriate price inde
M i l E iM i l E i
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Properties of a Short-Run Cubic
Cost Function
• verage variable cost & marginal
cost functions are, respectively:
= + +2 3TVC aQ bQ cQ
= + + 2
AVC a bQ cQ
= + + 2
SMC a 2bQ 3cQ
M i l E iM i l E i
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Properties of a Short-Run Cubic
Cost Function
• verage variable cost reaches its
minimum value at:
= + +2 3TVC aQ bQ cQ
= −m
Q b 2c
> < >0 0 0a , b , c and
• To conform to theoretical properties,
parameters must satisfy the following
restrictions:
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Summar$ of Short-Run Empirical
Production FunctionsShort-run cubic production e%uations
#otal product
$verage product of labor
%arginal product of labor
Diminishing marginalreturnsestrictions on
parameters
= +3 2
Q AL BL
= +2
AP AL BL
= +2
3 2 MP AL BL
< >0 0 A Band
= −
3m
B L A
begin at
M i l E iM i l E i
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Summar$ of Short-Run Empirical
Cost Functions Short-run cubiccost e%uations
#otal variable cost
$verage variable cost
%arginal cost
$verage variable costreaches minimum at
estrictions on
parameters
= + +2 3
TVC aQ bQ cQ
= + + 2
AVC a bQ cQ
= + + 2
2 3 SMC a bQ cQ
= −2
mbQc
> < >0 0 0a , b , c