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Production

ECO61 Microeconomic

AnalysisUdayan Roy

Fall 2008


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What is a firm?

A firm isan organization that convertsinputs such as labor, materials, energy,and capital into outputs, the goods andservices that it sells.

Sole proprietorshipsare firms owned and runby a single individual.

Partnershipsare businesses jointly owned andcontrolled by two or more people.

Corporationsare owned by shareholders inproportion to the numbers of shares of stockthey hold.


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What Owners Want?

Main assumption: firms owners tryto maximize profit

Profit ( ) isthe difference betweenrevenues, R, and costs, C:

= R C


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What are the categories ofinputs?

Capital (K) - long-lived inputs. land, buildings (factories, stores), and equipment

(machines, trucks)

Labor (L) - human services managers, skilled workers (architects,

economists, engineers, plumbers), and less-skilledworkers (custodians, construction laborers,assembly-line workers)

Materials (M) - raw goods (oil, water,wheat) and processed products (aluminum,plastic, paper, steel)


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How firms combine theinputs?

Production function is therelationship between the quantitiesof inputs used and the maximum

quantity of output that can beproduced, given current knowledgeabout technology and organization


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Production Function

Formally,

q = f(L, K)

where qunits of output are produced usingLunits of labor services and Kunits ofcapital (the number of conveyor belts).

ProductionFunction

q = f(L, K)

Outputq

Inputs(L, K)


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The production function maysimply be a table of numbers


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The production function maybe an algebraic formula

}12,24{min18

1224

15 4.06.0

KLQ

KLQ

KLQ

=+=

=

Just plug innumbers for L andKto get Q.


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Marginal Product of Labor

Marginal product of labor (MPL) - the

change in total output, Q, resultingfrom using an extra unit of labor, L,

holding other factors constant:

L

QMP

L

=


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Average Product of Labor

Average product of labor (APL) - the

ratio of output, Q, to the number ofworkers,L, used to produce that output:

L

QAP

L

=


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Production with Two VariableInputs

When a firm has more than onevariable input it can produce a givenamount of output with many different

combinations of inputs E.g., by substituting Kfor L

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Isoquants

An isoquantidentifies all inputcombinations (bundles) thatefficiently produce a given level of

output Note the close similarity to indifference

curves

Can think of isoquants as contour lines

for the hill created by the productionfunction

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Family ofIsoquants

K

,Unitsofc

apitalper

d

ay

e

b

a

d

fc

63210 L, Workers per day

6

3

2

1

q = 14

q = 24

q = 35

The production functionabove yields the isoquants

on the left.


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Figure 7.8: IsoquantExample

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ProductiveInputs Principle:Increasing theamounts of allinputs increasesthe amount ofoutput. So, anisoquant must benegatively sloped


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Properties of Isoquants

Isoquants are thin

Do not slope upward

Two isoquants do not cross Higher-output isoquants lie farther

from the origin

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Figure 7.10: Properties ofIsoquants

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Figure 7.10: Properties ofIsoquants

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Substitution Between Inputs

Rate that one input can be substituted foranother is an important factor for managers inchoosing best mix of inputs

Shape of isoquant captures information about

input substitution Points on an isoquant have same output but different

input mix

Rate of substitution for labor with capital is equal tonegative the slope

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Marginal Rate of TechnicalSubstitution

Marginal Rate of Technical Substitution forlabor with capital(MRTSLK): the amount of

capital needed to replace labor while keepingoutput unchanged, per unit of replaced labor

Let Kbe the amount of capital that can replace Lunits of labor in a way such that total output Q =F(L,K) is unchanged.

Then, MRTSLK = - K/ L, and

K/ L is the slope of the isoquant at thepre-change

inputs bundle.Therefore, MRTSLK = - slope of the isoquant


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Marginal Rate of TechnicalSubstitution

marginal rate of technicalsubstitution (MRTS) - the number ofextra units of one input needed toreplace one unit of another input thatenables a firm to keep the amount ofoutput it produces constant

L

KMRTS

==

laborinincrease

capitalinincrease

Slope of Isoquant!


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How the Marginal Rate of TechnicalSubstitution Varies Along an Isoquant

K,Unitsof

capitalpe

rd

ay

L, Workers per day

45

7

10

16a

b

c

d

eq = 10

K= 6

L = 1

0 1

1

1

1

2 3

3

2

1

4 5 6 7 8 9 10

MRTS in a Printing and Publishing U.S. Firm


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Substitutability of Inputs and MarginalProducts.

Along an isoquant output doesnt change ( q =0), or:

(MPLxL) + (MPKxK) = 0.

or

Increase in q per

extra unit of labor

Extra units

of labor

Increase in q per

extra unit of capital

Extra units

of capital

isoquantofslope

0

===

=

=

MRTSMP

MP

L

K

LMP

MPK

LMPKMP

K

L

K

L

LK


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Figure 7.12: MRTS

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MRTS and Marginal Product

Recall the relationship between MRSand marginal utility

Parallel relationship exists between

MRTS and marginal product

The more productive labor is relative tocapital, the more capital we must add tomake up for any reduction in labor; thelarger the MRTS

K

LLK

MP

MPMRTS =

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Figure 7.13: DecliningMRTS

We often assumethat MRTS

LK

decreases as weincrease L anddecrease K

Why is this a

reasonableassumption?

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Extreme ProductionTechnologies

Two inputs areperfect substitutes iftheir functions are identical

Firm is able to exchange one for another at a

fixed rate Each isoquant is a straight line, constant MRTS

Two inputs areperfect complementswhen

They must be used in fixed proportions

Isoquants are L-shaped

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Substitutability of Inputs


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Substitutability of Inputs


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Returns to Scale

Types of Returns to Scale Proportional change in ALLinputs yields

What happens when allinputs are doubled?

Constant Same proportional change inoutput

Output doubles

Increasing Greater than proportionalchange in output

Output more than doubles

Decreasing Less than proportional changein output Output less than doubles

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Figure 7.17: Returns toScale

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Returns to Scale

Constant returns to scale (CRS) -property of a production functionwhereby when all inputs are increased

by a certain percentage, outputincreases by that same percentage.

f(2L, 2K) = 2f(L, K).


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Returns to Scale (cont).

Increasing returns to scale (IRS)- property of a production functionwhereby output rises more than in

proportion to an equal increase in allinputs

f(2L, 2K) > 2f(L, K).


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Returns to Scale (cont).

Decreasing returns to scale(DRS) - property of a productionfunction whereby output increases

less than in proportion to an equalpercentage increase in all inputs

f(2L, 2K) < 2f(L, K).


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Productivity Differences andTechnological Change

A firm is more productive or hashigher productivitywhen it canproduce more output use the sameamount of inputs Its production function shifts upward at each

combination of inputs

May be either general change in productivityof specifically linked to use of one input

Productivity improvement that leavesMRTS unchanged is factor-neutral

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The Cobb-Douglas Production Function

It one is the most popular estimatedfunctions.

q =ALK


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Cobb-Douglas ProductionFunction

A shows firms general productivity level

and affect relative productivities oflabor and capital

Substitution between inputs:

1

1

=

=

KALMP

KALMP

K

L

( ) KALKLFQ == ,

=

L

KMRTSLK

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Figure: 7.16: Cobb-DouglasProduction Function

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