Behind the Supply Curve: Production Function I

8/9/2019 Behind the Supply Curve: Production Function I

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Behind The Supply Curve:Behind The Supply Curve:

Production Function IProduction Function I

1. Production - short run1. Production - short run

Productive efficiencyProductive efficiency

The Law of diminishing marginal returnsThe Law of diminishing marginal returns

2. Production - long run2. Production - long run

isoquants & isocostsisoquants & isocosts

least cost method of productionleast cost method of production


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BackgroundBackground

Firms seek to maximise profit (Firms seek to maximise profit ( )) = R - C= R - C

How do firms produce output andHow do firms produce output and

minimise costs (C)?minimise costs (C)?

What is production?What is production?production is simply the process ofproduction is simply the process of

transforming inputs and outputs.transforming inputs and outputs. inputs = capital (K) and labour (L)inputs = capital (K) and labour (L)


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A production functionA production function

Functional relationshipFunctional relationshipQ = f(K, L , T)Q = f(K, L , T)

T changes over timeT changes over time

At a point in time T is fixedAt a point in time T is fixed

Productive efficiencyProductive efficiencyA method of production is efficient if, for aA method of production is efficient if, for a

given level of factor inputs, it is impossiblegiven level of factor inputs, it is impossibleto obtain a higher level of output, given theto obtain a higher level of output, given the

existing state of technology.existing state of technology.


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The short runThe short run

Period of time over which one factor isPeriod of time over which one factor is

fixedfixedCapital - machines, factory, etc.Capital - machines, factory, etc.

Total and Marginal Physical ProductTotal and Marginal Physical Productmarginal product is the additional outputmarginal product is the additional output

produced by an additional unit of labourproduced by an additional unit of labour

MPP =MPP = TPP /TPP / LL

See FigureSee Figure


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figfig

0

1 0

2 0

3 0

4 0

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farmWheat production per year from a particular farm

Number of farm workers

Tonnes

ofwheatpro

d

uced

peryear

Number of

workers

0

1

2

3

4

5

67

8

TPP

03

10

24

36

40

4242

40


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figfig

0

1 0

2 0

3 0

4 0

0 1 2 3 4 5 6 7 8


Tonnes

ofwheatpro

d

uced

peryear TPP

farm

farm


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figfig

0

1 0

2 0

3 0

4 0

0 1 2 3 4 5 6 7 8


Tonnes

ofwheatpro

d

uced

peryear TPP

a

b

Diminishing returnsset in here

c

Maximum output

farm

farm


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figfig

0

10

20

30

40

0 1 2 3 4 5 6 7 8

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

farm

farm

T

onnes

ofwheatp

eryea

r

TPP

Tonnes

ofwheatperyea

r

MPP

Number offarm workers (L)

Number of

farm workers (L)


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figfig

b

b

d

0

10

20

30

40

0 1 2 3 4 5 6 7 8

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

T

onnes

ofwheatp

eryea

r

TPP

Tonnes

ofwheatperyea

r

APP

MPP

Diminishing

returns

set in here

Number offarm workers (L)

Number of

farm workers (L)

Maximumoutput

d

farm

farm


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Law of Diminishing ReturnsLaw of Diminishing Returns

DefinitionDefinitionas units of one input are added (with allas units of one input are added (with all

other inputs held constant), a point will beother inputs held constant), a point will be

reached where the resulting additions toreached where the resulting additions tooutput will begin to decrease; that isoutput will begin to decrease; that is

marginal productmarginal productwillwill declinedecline..

On figure - between 2 and 3 workersOn figure - between 2 and 3 workers


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2. The Long Run2. The Long Run

All factors are variableAll factors are variable

DecisionsDecisionsScaleScale

LocationLocation

TechniqueTechnique

Choice of techniqueChoice of techniqueIsoquantsIsoquantsIsocostsIsocosts


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IsoquantsIsoquants

An isoquantAn isoquantis a contour line which joins together theis a contour line which joins together the

different combinations of two factors ofdifferent combinations of two factors of

production that are just physically able toproduction that are just physically able toproduce a given quantity of a good.produce a given quantity of a good.

Construction, slope and mapsConstruction, slope and maps


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0

An isoquantAn isoquant

Units

of K40

20

10

6

4

Units

of L 5

12

20

30

50

Units of labour (L)

Unitso

fca

pital(K

)

A i


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0

Units

of K40

20

10

6

4

Units

of L 5

12

20

30

50

Point on

diagrama

b

c

d

e

a

b

c

de

Units of labour (L)

Unitso

fca

pital(K

)

An isoquantAn isoquant

f fDi i i hi i l t f f t b tit ti


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figfig

0

2

4

6

8

10

12

14

0 2 4 6 8 1 0 12 14 16 1 8 20 22

h

Unitso f

capital(K

)

Units of labour (L)

K= 2

L = 1

isoquant

MRS= 2 MRS= K / L

Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution

g

Di i i hi i l t f f t b tit tiDi i i hi i l t f f t b tit ti


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figfig

0

2

4

6

8

1 0

1 2

1 4

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

Unitso f

capital(K

)

Units of labour (L)

g

h

j

k

L = 1

K= 1

L = 1

isoquant

MRS= 2

MRS= 1

MRS= K / L

Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution

K= 2


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figfig

0

1 0

2 0

3 0

0 1 0 2 0

I1

I2

I3

I4

I5

Unitso f

capital(K

)

Units of labour (L)

An isoquant mapAn isoquant map


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IsocostsIsocosts

Actual output also depends on costsActual output also depends on costs

isocostsisocostsjoin combinations of K & L - same costjoin combinations of K & L - same cost

assuming constant factor pricesassuming constant factor prices

Construction, slope & mapConstruction, slope & map

A i tA i t


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

An isocostAn isocost

Units of labour (L)

Unitso

fca

pital(K

)

Assumptions

PK

= 20 000

W= 10 000

TC= 300 000

TC= 300 000

A i tA i t


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

Units of labour (L)

Unitso

fca

pital(K

)

TC= 300 000

a

b

c

d

An isocostAn isocost

Assumptions

PK

= 20 000

W= 10 000

TC= 300 000

Fi di th l t t th d f d tiFi di th l t t th d f d ti


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

3 5

0 1 0 2 0 3 0 4 0 5 0

Finding the least-cost method of productionFinding the least-cost method of production

Units of labour (L)

Unitso

fca

pital(K

)

Assumptions

PK = 20 000W= 10 000

TC= 200

000

TC= 300 000

TC= 400 000

TC= 500 000

Fi di th l t t th d f d tiFi di th l t t th d f d ti


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

3 5

0 1 0 2 0 3 0 4 0 5 0

Units of labour (L)

Unitso

fc

apital(K

)

TPP1


Fi di th l t t th d f d tiFinding the least cost method of prod ction


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figfig

0

5

1 0

1 5

2 0

2 5

3 0

3 5

0 1 0 2 0 3 0 4 0 5 0

Units of labour (L)

Unitso

fca

pital(K

)

TC= 400 000

TC= 500 000

s

r

tTPP1



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Least cost method of productionLeast cost method of production

Tangency between isoquant andTangency between isoquant and

isocostisocost

Where:Where:Slope of isoquant = slope of isocostSlope of isoquant = slope of isocost

Successive points of tangency -Successive points of tangency - scalescale

expansion pathexpansion path

Behind the Supply Curve: Production Function I

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