Isoquant Analysis

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Isoquant Analysis. Isoquant analysis. Constructing isoquants. An isoquant. Units of K 40 20 10 6 4. Units of L 5 12 20 30 50. Point on diagram a b c d e. Units of capital ( K ). Units of labour ( L ). An isoquant. a. Units of K 40 20 10 6 4. Units - PowerPoint PPT Presentation

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Isoquant AnalysisIsoquant Analysis

Isoquant analysisIsoquant analysis

Constructing isoquants

Constructing isoquants

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagram

abcde

Units of labour (L)

Un

its o

f ca

pita

l (K

)An isoquantAn isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagram

abcde

a

Units of labour (L)

Un

its o

f ca

pita

l (K

)An isoquantAn isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagram

abcde

a

b

Units of labour (L)

Un

its o

f ca

pita

l (K

)An isoquantAn isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagram

abcde

a

b

c

de

Units of labour (L)

Un

its o

f ca

pita

l (K

)An isoquantAn isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Isoquant analysisIsoquant analysis

Diminishing marginalrate of substitution

Diminishing marginalrate of substitution

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20

Un

its o

f ca

pita

l (K

)

Units of labour (L)

g

hK = 2

L = 1

isoquant

MRS = 2 MRS = K / L

Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20

Un

its o

f ca

pita

l (K

)

Units of labour (L)

g

h

j

k

K = 2

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

Isoquant analysisIsoquant analysis

An isoquant mapAn isoquant map

0

10

20

30

0 10 20

I1I2

I3

I4

I5

Un

its o

f ca

pita

l (K

)

Units of labour (L)

An isoquant mapAn isoquant map

Isoquant analysisIsoquant analysis

Returns to scaleReturns to scale

0

1

2

3

4

0 1 2 3

Un

its o

f ca

pita

l (K

)

Units of labour (L)

200

300

400

500

600

a

b

cR

Constant returns to scaleConstant returns to scale

0

1

2

3

4

0 1 2 3

Un

its o

f ca

pita

l (K

)

Units of labour (L)

200

300

400

500

600

a

b

cR

700

Increasing returns to scale (beyond point b)Increasing returns to scale (beyond point b)

0

1

2

3

4

0 1 2 3

Un

its o

f ca

pita

l (K

)

Units of labour (L)

200

300

400

500

a

b

cR

Decreasing returns to scale (beyond point b)Decreasing returns to scale (beyond point b)

Isoquant analysisIsoquant analysis

IsocostsIsocosts

Units of labour (L)

Un

its o

f ca

pita

l (K

)

Assumptions

PK = £20 000 W = £10 000

TC = £300 000

An isocostAn isocost

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

Units of labour (L)

Un

its o

f ca

pita

l (K

)

TC = £300 000

a

b

c

d

Assumptions

PK = £20 000 W = £10 000

TC = £300 000

An isocostAn isocost

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

Isoquant analysisIsoquant analysis

The least-costmethod of production

The least-costmethod of production

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 method of productionFinding the least-cost method of production

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 method of productionFinding the least-cost method of production

Isoquant analysisIsoquant analysis

Effect of a rise inthe wage rate

Effect of a rise inthe wage rate

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

24

r

Assumptions

PK = £20 000W = £10 000

Effect of a wage rise on the least-cost method of productionEffect of a wage rise on the least-cost method of production

8

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

r

Assumptions

PK = £20 000W = £10 000

= £20 000

Effect of a wage rise on the least-cost method of production(wage rises to £20 000)

Effect of a wage rise on the least-cost method of production(wage rises to £20 000)

24

8

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

8r

Assumptions

PK = £20 000W = £10 000

= £20 000

TC = £400 00011

9

r

Effect of a wage rise on the least-cost method of production(wage rises to £20 000)

Effect of a wage rise on the least-cost method of production(wage rises to £20 000)

24

Isoquant analysisIsoquant analysis

The maximum outputfor a given cost

The maximum outputfor a given cost

TPP2

TPP3

TPP4

TPP5

Un

its o

f ca

pita

l (K

)

Units of labour (L)

OTPP1

Finding the maximum output for a given total costFinding the maximum output for a given total cost

O

Isocost

Un

its o

f ca

pita

l (K

)

Units of labour (L)

TPP2

TPP3

TPP4

TPP5

TPP1

Finding the maximum output for a given total costFinding the maximum output for a given total cost

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 output for a given total costFinding the maximum output for a given total cost

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 output for a given total costFinding the maximum output for a given total cost

t

Isoquant analysisIsoquant analysis

Deriving an LRAC curve from an isoquant map

Deriving an LRAC curve from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

TC1

100TC

2

200

At an output of 200LRAC = TC2 / 200

Deriving an LRAC curve from an isoquant mapDeriving an LRAC curve from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

TC1

TC2

TC3

TC4

TC5

TC6

TC7

100 200300

400500

600

700

Note: increasing returnsto scale up to 400 units;

decreasing returns toscale above 400 units

Deriving an LRAC curve from an isoquant mapDeriving an LRAC curve from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

TC1

TC2

TC3

TC4

TC5

TC6

TC7

100 200300

400500

600

700

Expansion path

Deriving an LRAC curve from an isoquant mapDeriving an LRAC curve from an isoquant map

Isoquant analysisIsoquant analysis

Deriving short-run costs from an isoquant map

Deriving short-run costs from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

100

200

300

TC =£20 000

TC =£40 000

TC =£60 000

The long-run situation:both factors variable

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

The long-run situation:both factors variable

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

K1

The short-run situation:capital fixed in supply

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

K1

L1

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

TC =£22 000

K1

L2 L1

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

TC =£65 000

TC =£22 000

K1

L2 L1 L3

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

L4

K2

Un

its o

f ca

pita

l (K

)

O

Units of labour (L)

100

200

300

Expansion path

TC =£20 000

TC =£40 000

TC =£60 000

TC =£65 000

TC =£22 000

K1

L2 L1 L3

a

bL

bS

Deriving short-run costs from an isoquant mapDeriving short-run costs from an isoquant map

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