behind the supply curve: production function i 1. production - short run 1. production - short run...
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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
BackgroundBackground
Firms seek to maximise profit (Firms seek to maximise profit () ) = R - C= R - C
How do firms produce output and How do firms produce output and minimise costs (C)?minimise costs (C)?
What is production?What is production?“…“…production is simply the process of production 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)
A production functionA production function
Functional relationshipFunctional relationshipQ = f(K, L , T) Q = f(K, L , T) T changes over time T changes over time At a point in time T is fixedAt a point in time T is fixed
Productive efficiencyProductive efficiency““A method of production is efficient if, for a A method of production is efficient if, for a
given level of factor inputs, it is impossible given level of factor inputs, it is impossible to obtain a higher level of output, given the to obtain a higher level of output, given the existing state of technology.”existing state of technology.”
The short runThe short run
Period of time over which one factor Period of time over which one factor is fixed is fixed
Capital - machines, factory, etc.Capital - machines, factory, etc.
Total and Marginal Physical ProductTotal and Marginal Physical Product“…“…marginal product is the additional output marginal product is the additional output
produced by an additional unit of labourproduced by an additional unit of labourMPP = MPP = TPP / TPP / LL
See FigureSee Figure
figfig
0
10
20
30
40
0 1 2 3 4 5 6 7 8
Number of farm workers
To
nne
s o
f wh
eat
pro
du
ced
pe
r ye
ar TPP
Wheat production per year from a particular farm
Wheat production per year from a particular farm
figfig
0
10
20
30
40
0 1 2 3 4 5 6 7 8
-2
0
2
4
6
8
10
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0 1 2 3 4 5 6 7 8
Wheat production per year from a particular farm
Wheat production per year from a particular farm
Ton
nes
of w
heat
per
yea
r
TPP
Ton
nes
of w
heat
per
yea
r
MPP
Number offarm workers (L)
Number offarm workers (L)
Law of Diminishing ReturnsLaw of Diminishing Returns
Definition Definition “…“…as units of one input are added (with all as units of one input are added (with all
other inputs held constant), a point will be other inputs held constant), a point will be reached where the resulting additions to reached where the resulting additions to output will begin to decrease; that is output will begin to decrease; that is marginal productmarginal product will will declinedecline.”.”
On figure - between 2 and 3 workers On figure - between 2 and 3 workers
2. The Long Run2. The Long Run
All factors are variableAll factors are variable DecisionsDecisions
ScaleScaleLocationLocationTechniqueTechnique
Choice of techniqueChoice of technique IsoquantsIsoquants IsocostsIsocosts
Isoquants Isoquants
An isoquantAn isoquant“…“…is a contour line which joins together the is a contour line which joins together the
different combinations of two factors of different combinations of two factors of production that are just physically able to production that are just physically able to produce a given quantity of a good.”produce a given quantity of a good.”
Construction, slope and maps Construction, slope and maps
figfig
0
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0 5 10 15 20 25 30 35 40 45 50
An isoquantAn isoquant
Unitsof K
402010 6 4
Unitsof L 512203050
Units of labour (L)
Un
its o
f ca
pita
l (K
)
figfig
0
2
4
6
8
10
12
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0 2 4 6 8 10 12 14 16 18 20 22
h
Un
its o
f ca
pita
l (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
figfig
0
10
20
30
0 10 20
I1I2I3I4
I5
Un
its o
f ca
pita
l (K
)
Units of labour (L)
An isoquant mapAn isoquant map
IsocostsIsocosts
Actual output also depends on costsActual output also depends on costs isocostsisocosts
join combinations of K & L - same costjoin combinations of K & L - same costassuming constant factor pricesassuming constant factor prices
Construction, slope & mapConstruction, slope & map
figfig
0
5
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25
30
0 5 10 15 20 25 30 35 40
An isocostAn isocost
Units of labour (L)
Un
its o
f ca
pita
l (K
)
Assumptions
PK = £20 000 W = £10 000
TC = £300 000
TC = £300 000
figfig
0
5
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15
20
25
30
35
0 10 20 30 40 50
Finding the least-cost method of productionFinding the least-cost method of production
Units of labour (L)
Un
its o
f ca
pita
l (K
)
Assumptions
PK = £20 000W = £10 000
TC = £200 000
TC = £300 000
TC = £400 000
TC = £500 000
figfig
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Units of labour (L)
Un
its o
f ca
pita
l (K
)
TPP1
Finding the least-cost method of productionFinding the least-cost method of production
Least cost method of productionLeast cost method of production
Tangency between isoquant and Tangency 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 - scale scale expansion pathexpansion path
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