theory of isoquants returns to scale 2011

8/3/2019 Theory of Isoquants Returns to Scale 2011

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Production Function with

two variable inputs


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The optimum combination offactors: the marginal

product approach


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The optimum combination of factors:

the marginal product approach

Long run all factors are variable

Profit maximizing firm will want to

use the least costly combination offactors to produce any output

What is the optimum combination offactors?


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The simple two factor case

Firm uses just two factors: Labour:l &Capital:k

Least cost combination will be where MPPl/Pl = MPPk/Pk

If they were not equal it would be

possible to reduce cost per unit ofoutput by using a differentcombination of labor & capital


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The multi-factor case

Where a firm uses many factors least costcombination of factors will be where:

MPPa/Pa =MPPb/Pb =MPPc/Pc.MPPn/Pn


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The optimum combination offactors: the

isoquant/isocost approach


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The

Technology of Production

The production function for twoinputs:

Q = F(K,L)

Q = Output, K = Capital, L =Labor

For a given technology


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Isoquants or Equal

Product curves Isoquants

Curves showing all possible combinations of inputs that yieldthe same output

It is the production function of a product with two factorsvariable

It represents the technical conditions of production

Some similarities with indifference curves

Also called production indifference curves

Indifference curves no attempt made to specify the level ofsatisfaction to a consumer but in isoquants we can label inphysical units of output


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fig

Unitsof K

40

20

10

6

4

Unitsof L

5

12

20

30

50

Point ondiagram

a

b

c

d

e

a

b

cd

e

Units of labour (L)

Unitsofcap

ital(K)

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

An isoquantAn isoquant


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Production Function for Food

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Capital Input 1 2 3 4 5

Labor Input


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Production with Two Variable Inputs (L,K)

Labor per year

1

2

3

4

1 2 3 4 5

5

Q1= 55

The isoquants are derivedfrom the production

function for output of

of 55, 75, and 90.A

D

B

Q2= 75

Q3= 90

C

E

Capital

per year The Isoquant Map


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Assumptions

Producer uses only two inputs- L & K

L & K can be substituted for one

another at a diminishing rate Constant Technology

L & K are perfectly divisible &

substitutable- continuous isoquant


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Isoquants: PropertiesIsoquants: Properties

Slope downwards from left to right-negative slope

No two equal product curves canintersect each other

Convex to the origin: diminishing

MRTS


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Marginal Rate ofTechnical

Substitution MRTS of factor X for factor Y may be

defined as the amount of factor Ywhich can be replaced by a unit of

factor X, the level of outputremaining unchanged It can be known from the slope of the

isoquant

Diminishing MRTS: As the quantityof X is increased and the quantity of Yis decreased the amount of factor Ythat is required to be replaced by anadditional unit of X so as to keep the

output constant will diminish


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fig

Unitsofc

apital(K)

Units of labour (L)

g

h(K=2

(L =1

isoquant

MRS=2 MRS=(K /(L

Diminishing marginal rate offactor substitution

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22


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fig

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20

Unitsofc

apital(K)

Units of labour (L)

g

h

j

k

(K=2

(L =1

(K=1

(L =1

isoquant

MRS=2

MRS=1

MRS=(K /(L

Diminishing marginal rate offactor substitutionDiminishing marginal rate offactor substitution


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I

socost lines Shows various combinations of two

factors that the firm can buy with agiven or same outlay/cost

Assume that prices of factors aregiven and constant for the firm

Isocost line will shift if the totaloutlay of the firm changes or theprices of factors change


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fig

Units of labour (L)

Unitsofcap

ital(K)

TC= 300000

a

b

c

d

Assumptions

PK= 20000

W= 10000

TC= 300000

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

An isocostAn isocost


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Least-cost combination of factors for a given output

point of tangency of the isoquant with an iso cost

line

At this point MRTS = Px/Py

Minimizing cost when he uses a factor combination

for which his MRTS is equal to the price ratio of thefactors

Tangency point of the given isoquant with an isocost line represents the least cost combination offactors for producing a given output

ISOQUANT- ISOCOSTANALYSISISOQUANT- ISOCOSTANALYSIS


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fig

Units of labour (L)

Unitsofcap

ital(K)

Assumptions

PK= 20000

W= 10000

TC= 200000

TC= 300000

TC= 400000

TC= 500000

Finding the least-cost methodof production

0

5

10

15

20

25

30

35

0 10 20 30 40 50


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fig

O

K1

L1

Unitsofca

pital(K)

Units of labour (L)

TPP2

TPP3

TPP4

TPP5

r

v

s

u

TPP1

t

Finding the maximum outputfor a given total costFinding the maximum outputfor a given total cost


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Production Function with

all variable inputs


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Production Function with allvariable inputs

A situation where all inputs aresubject to variation

In case of law of variable proportionssome inputs are constant while inReturns to scale all inputs change inthe same proportion


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The Long run productionFunction

The long-run productionfunction describes the

maximum quantity of good orservice that can be produced bya set of inputs, assuming that

the firmis free to adjust the levelofallinputs.


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Production in the Long Run

In the long run, all inputs are variable.

The long run production process isdescribed by the concept ofReturns to

Scale. Returns to scale describes what happens

to total output as all of the inputs arechanged by the same proportion.

Q = f(K,L)


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Production Function & Returns to

Scale Production function is homogeneous means that all

inputs are increased in same proportion

If all inputs are increased in a certain proportion(say k) & output increases in the same proportionthe production function is homogeneous of degree1- also known as Linear Homogeneous ProductionFunction

Can be expressed as

kQx = f(kK, kL)

= k (K, L)

This implies constant returns to scale

Cobb-Douglas production function is homogeneous

of degree 1


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Production Function &

Returns to Scale If all inputs are increased in a certain

proportion total output may not increasein the same proportion, it may increaseby less than or more than double

This can be expressed as

hQx = f (kK, kL) where h denotes h

increase in Qx due to k increase ininputs K, L

The proportion h may be greater than,equal to, or less than k


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Production Function &

Returns to Scale Accordingly there are three Returns to scale

The word to scale means that all inputsincrease by the same proportion

If h = k, production function reveals constantreturns to scale

If h is greater than k it reveals increasingreturns to scale

If h is less than k it reveals decreasing returnsto scale


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What are Increasing returns to scaleor Economies of scale?

Output changes disproportionately more in

comparison to a change in the scale of input Output can more than double if inputs are

doubled

A situation in which the costs per unit of

output fall as the scale of productionincreases


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Causes of Economies of Scale

INTERNAL ECONOMIES OF SCALE : REAL& PECUNIARY

Real Economies: when quantity of inputs

used decreases for a given level of output Pecuniary Economies: savings in expenses

due to relatively lower prices for inputs &lower cost of distribution due to bulk buying& selling


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REAL ECONOMIES

Production Economies: Division of labor Specialization & time saving

Cumulative volume experience in technicalwork Technical economies- specialization of capital,

indivisibilities, economies of large machines Dimensional relations: e.g. when size of a

room (15

feet x10

feet =150

sq ft) is doubledto 30 x 20 then the area of the room is morethan doubled i.e. 30 feet x 20 feet = 600 sq ft

Inventory economies for raw materials & finalgoods


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INTERNAL ECONOMIES OF SCALE :REAL Economies.

Marketing Economies: Advertising & selling activities Exclusive dealers with after sales service

obligations Variations in models & designs- more of R &DManagerial economies: Specialization of management Teamwork experience

Decentralization Modern managerial & organizational techniquesTransport & Storage economies


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INTERNAL ECONOMIES OF SCALE:

PECUNIA

RY

ECON

OMI

ES

Discounts a firm can get due to its largesize

Discounts in raw materials Lower cost of funds

Lower cost of advertising

Lower transport cost


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External Economies of Scale:

Where a firms costs per unit of outputdecrease as the size of the whole industrygrows

Where a firm whatever its size benefitsfrom the whole industry being large

Specialized firms for working up the by-product & waste materials

Specialized units to supply raw materials ,research etc


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External Economies of Scale

Industry's Infrastructure:

The network of supply agents:

communications, skills, training,distribution channels, specializedfinancial services etc


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What are Constant returns toscale?

Output changes in a fixed proportion to thechange in total inputs.

Output can exactly double if inputs aredoubled

A situation in which the long-run averagecost curve does not change as the firmincreases output


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Causes of Constant returnsto scale

Limits of the economies of scale

When economies disappear &

diseconomies are yet to begin thenconstant returns


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What are decreasing returns toscale or diseconomies of scale?

Output changes disproportionately

less compared to a change in the

scale of inputs

Output can less than double if inputs

are doubled

A situation in which the long-run

average cost curve rises as the firm

increases output


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Diseconomies of Scale

Technical factors unlikely to producediseconomies of scale

Diseconomies more associated withhuman & behavioral problems ofmanaging a large enterprise

Control loss- quantity of information

received & transmitted per unit ofoutput is less after expansion

Spirit in large firm is less than small

firm due to lack of personal touch


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Causes ofDecreasingreturns to scale

Managerial diseconomies- diminishingreturns to management

As size of firm increases managerialefficiency decreases

Limitedness or exhaustibility ofnatural resources


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Rs40

Rs30

Rs20

Rs10

2 4 6 8

Rs50

Rs60

Rs70

Rs80

10 12 14 16 18

Long-run Average Cost Curve

Constant returns to scale

Diseconomies of scale

Economies of scale

Q


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Modern view: L shaped Long RunAverage Cost curve

Long run cost can be divided into Productioncost & Managerial cost

Modern theory says long run cost curve likely

to be L shaped than U shaped Production costs fall continuously with

increases in output while Managerial costs mayrise at very large scales of output

The fall in production costs more than offsetsthe increase in managerial costs, so that LACcontinuously falls with increases in scale


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Pause for a Thought

What economies of scale is alarge department store likely to

experience?


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Pause for a Thought

Specialised staff for each department (savingon training costs and providing a more efficientservice for customers); being able to reallocate

space as demand shifts from one product toanother and thereby reducing the overallamount of space required; full use of largedelivery lorries which would be able to carry arange of different products; bulk purchasing

discounts; reduced administrative overheadsas a proportion of total costs.


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Pause for a Thought

Name some industries where externaleconomies of scale are gained. What arethe specific external economies in each

case?


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Pause for a Thought

Two examples are:

Financial services: pool of qualified andexperienced labour, access to specialistsoftware, one firm providing specialistservices to another.

Various parts of the engineering industry:

pool of qualified and experienced labour,access to specialist suppliers, possiblejoint research, specialised bankingservices.


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Pause for a Thought

Would you expect external economiesto be associated with the concentrationof an industry in a particular region?


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Pause for a Thought

Yes. There may be a common transportand communications infrastructure thatcan be used; there is likely to be a pool

of trained and experienced labour in thearea; joint demand may be high enoughto allow economies of scale to beexperienced in the supply of somelocally extracted raw material.

theory of isoquants returns to scale 2011

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