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Isocost/Isoquant Isocost/Isoquant AnalysisAnalysis
Chapter 10 Appendix
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The Isocost/Isoquant The Isocost/Isoquant GraphGraph The analyst creates a graph showing
various combinations of factors of production that can produce a certain amount of output.
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The Isocost/Isoquant The Isocost/Isoquant GraphGraph
More than 3 units of machinery and more than 4 units of labor
Less than 3 units of machinery and less than 4 units of labor
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The Isoquant CurveThe Isoquant Curve
Isoquant curve – a curve that represents combinations of factors of production that results in equal amounts of output.
A point on the isoquant curve is technically efficient.
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The Isoquant CurveThe Isoquant Curve
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The Isoquant CurveThe Isoquant Curve
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The Isoquant CurveThe Isoquant Curve
The isoquant curve is bowed inward because of the law of diminishing marginal productivity.
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The Isoquant CurveThe Isoquant Curve
Marginal rate of substitution – the rate at which one factor must be added to compensate for the loss of another factor, to keep output constant.
It is the slope of the isoquant curve.
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The Isoquant CurveThe Isoquant Curve
The absolute value of the slope at a point on the isoquant curve equals the ratio of the marginal productivity of labor to the marginal productivity of machines.
onsubstituti of rate MarginalMP
MPSlope
machine
labor
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The Isoquant CurveThe Isoquant Curve
Isoquant map – a set of isoquant curves that show technically efficient combinations of inputs that can produce different levels of output.
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An Isoquant MapAn Isoquant Map
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Isoquants and Isoquants and indifference curvesindifference curves have most of the same properties biggest difference:
isoquant holds something measurable, quantity, constant
indifference curve holds something that is unmeasurable, utility, constant
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3 major properties of 3 major properties of isoquantsisoquants follow from the assumption that
production is efficient:
1. further an isoquant is from the origin, the greater is the level of output
2. isoquants do not cross
3. isoquants slope down
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Shape of isoquantsShape of isoquants
curvature of isoquant shows how readily a firm can substitute one input for another
extreme cases: perfect substitutes: q = x + y fixed-proportions (no substitution): q = min(x, y)
usual case: bowed away from the origin
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Perfect Substitutes: Fixed Perfect Substitutes: Fixed ProportionsProportions
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Cannot be SubstitutedCannot be Substituted
Complementary inputs MRTS=0
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The Isocost LineThe Isocost Line
Isocost line – a line that represents alternative combinations of factors of production that have the same costs.
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The Isocost LineThe Isocost Line
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Choosing the Choosing the Economically Efficient Economically Efficient Point of ProductionPoint of Production The least cost combination of inputs for a
given output occurs where the isocost curve is tangent to the isoquant curve for that output.
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Choosing the Choosing the Economically Efficient Economically Efficient Point of ProductionPoint of Production
machines
machines
labor
labor
machines
labor
machines
labor
P
MP
P
MP that so
P
P–
MP
MP–
The slopes of the two curves are equal at that point of tangency.
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Choosing the Choosing the Economically Efficient Economically Efficient Point of ProductionPoint of Production The firm is operating efficiently when an
additional output per dollar spent on labor equals the additional output per dollar spent on machines.
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Recall: Production IsoquantsRecall: Production Isoquants
Isoquants show the substitution between capital and labour that is required to maintain a particular level of output.
The slope of an isoquant is - MPPL/MPPK
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Producer EquilibriumProducer Equilibrium
This graph shows a firm minimizing cost subject to an output constraint. The constraint is represented by isoquant Q=100 units of output.
Isocost curve
slope is -w/r
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Isoquant analysisIsoquant analysis
The least-cost
method of production
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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
)
Assumptions
PK = £20 000W = £10 000
TC = £200 000
TC = £300 000
TC = £400 000
TC = £500 000
Finding the least-cost Finding the least-cost method of productionmethod of production
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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
TC = £400 000
TC = £500 000
r
s
t
Finding the least-cost Finding the least-cost method of productionmethod of production
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Isoquant analysisIsoquant analysis
The maximum output
for a given cost
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TPP2
TPP3
TPP4
TPP5
Un
its o
f ca
pita
l (K
)
Units of labour (L)
OTPP1
Finding the maximum Finding the maximum output for a given total output for a given total costcost
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O
Isocost
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP2
TPP3
TPP4
TPP5
TPP1
Finding the maximum Finding the maximum output for a given total output for a given total costcost
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O
s
u
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP2
TPP3
TPP4
TPP5
r
v
TPP1
Finding the maximum Finding the maximum output for a given total output for a given total costcost
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O
K1
L1
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP2
TPP3
TPP4
TPP5
r
v
s
u
TPP1
Finding the maximum Finding the maximum output for a given total output for a given total costcost
t
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Combining Isoquant and Combining Isoquant and Isocost CurvesIsocost Curves
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Isocost/Isoquant Isocost/Isoquant AnalysisAnalysis
End of Chapter 10 Appendix