behind the supply curve: production function i
TRANSCRIPT
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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
Number of farm workers
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
Number of farm workers
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
Finding the least-cost method of productionFinding the least-cost method of production
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
Finding the least-cost method of productionFinding the least-cost method of production
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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