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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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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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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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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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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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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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Importance of production functions inmanagerial decision making

Application: Chinas workers

is China running out of workers? industrial boom eg bicycle factory in GuangdongProvence