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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 1
Chapter 6
The Theory
andEstimation of Production
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 2
Overview
The production functionShort-run analysis of averageand marginal productLong-run production functionImportance of productionfunction in managerial decisionmaking
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 4
Learning objectives
understand the law of diminishing returns
use the Three Stages of Production toexplain why a rational firm always tries tooperate in Stage II
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 5
Production functionProduction function: defines therelationship between inputs and themaximum amount that can be producedwithin a given period of time with a givenlevel of technology
Q=f(X 1 , X 2 , ..., X k)
Q = level of outputX1 , X 2 , ..., X k = inputs used in
production
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 6
Production functionKey assumptions
given state of the art productiontechnology
whatever input or input combinations
are included in a particular function, theoutput resulting from their utilization isat the maximum level
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 7
Production functionFor simplicity we will often consider aproduction function of two inputs:
Q=f(X, Y)Q = outputX = labor
Y = capital
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 9
Short-run analysis of Total, Average, and Marginal product
Alternative terms in reference to inputs inputs factors
factors of production resources
Alternative terms in reference to outputs
output quantity (Q) total product (TP) product
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 10
Short-run analysis of Total, Average, and Marginal product
Marginal product (MP) = change inoutput (Total Product) resulting from aunit change in a variable input
Average product (AP) = Total Productper unit of input used
X Q MP X
X Q
AP X
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 11
Short-run analysis of Total, Average, and Marginal product
if MP > AP then APis rising
if MP < AP then APis falling
MP=AP when AP ismaximized
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 12
Short-run analysis of Total, Average, and Marginal product
Law of diminishing returns : asadditional units of a variable input arecombined with a fixed input, after some
point the additional output (i.e., marginalproduct) starts to diminish
nothing says when diminishing returnswill start to take effectall inputs added to the productionprocess have the same productivity
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 13
Short-run analysis of Total, Average, and Marginal product
The Three Stages of Production in theshort run:
Stage I: from zero units of the variableinput to where AP is maximized (whereMP=AP)Stage II: from the maximum AP to
where MP=0Stage III: from where MP=0 on
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall. 14
Short-run analysis of Total, Average, and Marginal product
In the short run, rational firms should beoperating only in Stage II
Q: Why not Stage III? firm uses morevariable inputs to produce less output
Q: Why not Stage I? underutilizingfixed capacity, so can increase outputper unit by increasing the amount of thevariable input
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Short-run analysis of Total, Average, and Marginal product
What level of input usage within Stage IIis best for the firm?
answer depends upon: how many units of output the firm can sell the price of the product the monetary costs of employing the
variable input
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Short-run analysis of Total, Average, and Marginal product
Total revenue product (TRP) = marketvalue of the firms output, computed by
multiplying the total product by themarket price
TRP = Q P
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Short-run analysis of Total, Average, and Marginal product
Marginal revenue product (MRP) =change in the firms TRP resulting from a
unit change in the number of inputs used
MRP = MP P = X TRP
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Short-run analysis of Total, Average, and Marginal product
Total labor cost (TLC) = total cost ofusing the variable input labor, computedby multiplying the wage rate by thenumber of variable inputs employed
TLC = w X
Marginal labor cost (MLC) = change intotal labor cost resulting from a unit
change in the number of variable inputsusedMLC = w
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Short-run analysis of Total, Average, and Marginal product
Summary of relationship between demandfor output and demand for a single input:
A profit-maximizing firm operating in perfectlycompetitive output and input markets will beusing the optimal amount of an input at thepoint at which the monetary value of the
inputs marginal product is equal to theadditional cost of using that input
MRP = MLC
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Long-run production functionIn the long run, a firm has enough time tochange the amount of all its inputs
The long run production process isdescribed by the concept of returns toscale
Returns to scale = the resulting increasein total output as all inputs increase
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Long-run production functionIf all inputs into the production processare doubled, three things can happen:
output can more than double
increasing returns to scale (IRTS)
output can exactly double constant returns to scale (CRTS)
output can less than double decreasing returns to scale (DRTS)
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsExamples of production functions
short run: one fixed factor, one variable factorQ = f(L) K
cubic: increasing marginal returns followed bydecreasing marginal returns
Q = a + bL + cL 2 dL 3
quadratic: diminishing marginal returns but noStage IQ = a + bL - cL 2
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsExamples of production functions
power function: exponential for one input
Q = aLb
if b > 1, MP increasingif b = 1, MP constantif b < 1, MP decreasing
Advantage: can be transformed into a linear(regression) equation when expressed in log
terms
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsExamples of production functions
Cobb-Douglas function: exponential for
two inputsQ = aL bKc
if b + c > 1, IRTSif b + c = 1, CRTSif b + c < 1, DRTS
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsCobb-Douglas production functionAdvantages:
can investigate MP of one factor
holding others fixedelasticities of factors are equal to theirexponentscan be estimated by linear regressioncan accommodate any number ofindependent variablesdoes not require constant technology
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsCobb-Douglas production functionShortcomings:
cannot show MP going through all
three stages in one specificationcannot show a firm or industrypassing through increasing, constant,and decreasing returns to scale
specification of data to be used inempirical estimates
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsStatistical estimation of productionfunctions
inputs should be measured as flow
rather than stock variables, which isnot always possibleusually, the most important input islabor
most difficult input variable is capitalmust choose between time series andcross-sectional analysis
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Estimation of production functionsAggregate production functions: wholeindustries or an economy
gathering data for aggregate functions
can be difficult: for an economy GDP could be used for an industry data from Censusof Manufactures or production index
from Federal Reserve Board for labor data from Bureau ofLabor Statistics
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Importance of production functions inmanagerial decision making
Capacity planning : planning the amountof fixed inputs that will be used along withthe variable inputs
Good capacity planning requires:
accurate forecasts of demand
effective communication between theproduction and marketing functions
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Importance of production functions inmanagerial decision making
Example: cell phones
Asian consumers want new phoneevery 6 months demand for 3G products Nokia, Samsung, SonyEricsson mustbe speedy and flexible
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Importance of production functions inmanagerial decision making
Example: Zara
Spanish fashion retailer factories located close to stores quick response time of 2-4 weeks
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Importance of production functions inmanagerial decision making
Application: call centers
service activity production function is
Q = f(X,Y)where Q = number of calls
X = variable inputsY = fixed input
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Chapter Six Copyright 2009 Pearson Education, Inc.Publishing as Prentice Hall.
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Importance of production functions inmanagerial decision making
Application: Chinas workers
is China running out of workers? industrial boom eg bicycle factory in GuangdongProvence
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