McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Isocost/Isoquant Isocost/Isoquant AnalysisAnalysis

Chapter 10 Appendix

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

The Isoquant CurveThe Isoquant Curve

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

The Isoquant CurveThe Isoquant Curve

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

The Isoquant CurveThe Isoquant Curve

The isoquant curve is bowed inward because of the law of diminishing marginal productivity.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

An Isoquant MapAn Isoquant Map

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Perfect Substitutes: Fixed Perfect Substitutes: Fixed ProportionsProportions

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Cannot be SubstitutedCannot be Substituted

Complementary inputs MRTS=0

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

The Isocost LineThe Isocost Line

Isocost line – a line that represents alternative combinations of factors of production that have the same costs.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

The Isocost LineThe Isocost Line

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Isoquant analysisIsoquant analysis

The least-cost

method of production

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Isoquant analysisIsoquant analysis

The maximum output

for a given cost

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Combining Isoquant and Combining Isoquant and Isocost CurvesIsocost Curves

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Isocost/Isoquant Isocost/Isoquant AnalysisAnalysis

End of Chapter 10 Appendix