Isoquant Analysis
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Isoquant Analysis
Isoquant analysis
Constructing isoquants
An isoquant
45 40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
b
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
b
20 15
c
10
d
e
5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
Isoquant analysis
Diminishing marginal rate of substitution
Diminishing marginal rate of factor substitution 14
g
Units of capital (K)
12 ∆K = 2
MRS = ∆K / ∆L
MRS = 2 h
10 ∆L = 1
8 6 4 2
isoquant
0 0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Diminishing marginal rate of factor substitution 14
g
Units of capital (K)
12 ∆K = 2
MRS = ∆K / ∆L
MRS = 2 h
10 ∆L = 1
8
j
MRS = 1 k
∆K = 1
6
∆L = 1
4 2
isoquant
0 0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Isoquant analysis
An isoquant map
An isoquant map
Units of capital (K)
30
20
10
I5 I1
0 0
10
Units of labour (L)
I2 20
I3
I4
Isoquant analysis
Returns to scale
Constant returns to scale
4
Units of capital (K)
R c
3
b
2
500
400
a
1
600
300 200
0 0
1
2
Units of labour (L)
3
Increasing returns to scale (beyond point b)
4
Units of capital (K)
R c
3
700 600
b
2
500 400
a
1
300 200
0 0
1
2
Units of labour (L)
3
Decreasing returns to scale (beyond point b)
4
Units of capital (K)
R c
3
500
b
2
400
a
1
300 200
0 0
1
2
Units of labour (L)
3
Isoquant analysis
Isocosts
An isocost
30
Assumptions
Units of capital (K)
25
PK = £20 000 W = £10 000 TC = £300 000
20
15
10
5
0 0
5
10
15
20
25
Units of labour (L)
30
35
40
An isocost
30
Assumptions
Units of capital (K)
25
PK = £20 000 W = £10 000 TC = £300 000
20
a
15
b
10
c
5
TC = £300 000 d
0 0
5
10
15
20
25
Units of labour (L)
30
35
40
Isoquant analysis
The least-cost method of production
Finding the least-cost method of production 35
Assumptions
Units of capital (K)
30
PK = £20 000 W = £10 000
25
TC = £200 000 TC = £300 000
20 15
TC = £400 000 10
TC = £500 000
5 0 0
10
20
30
Units of labour (L)
40
50
Finding the least-cost method of production 35
Units of capital (K)
30 25
s
TC = £500 000
20 15
TC = £400 000
r
10
t
5
TPP1
0 0
10
20
30
Units of labour (L)
40
50
Isoquant analysis
Effect of a rise in the wage rate
Effect of a wage rise on the least-cost method of production 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000
25 20 15
TC = £400 000 10
r
8 5
TPP1 0 0
10
20
24
30
Units of labour (L)
40
50
Effect of a wage rise on the least-cost method of production (wage rises to £20 000) 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000 = £20 000
25 20 15
TC = £400 000 10
r
8 5
TPP1 0 0
10
20
24
30
Units of labour (L)
40
50
Effect of a wage rise on the least-cost method of production (wage rises to £20 000) 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000 = £20 000
25 20 15
TC = £400 000
r
1
10 1
r
8 5
TPP1 0 0
910
20
24
30
Units of labour (L)
40
50
Isoquant analysis
The maximum output for a given cost
Units of capital (K)
Finding the maximum output for a given total cost
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Units of capital (K)
Finding the maximum output for a given total cost
Isocost
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Finding the maximum output for a given total cost r Units of capital (K)
s
u v
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Finding the maximum output for a given total cost r Units of capital (K)
s
K1
t
u v O
TPP5 TPP4 TPP3 TPP2
TPP1 L1 Units of labour (L)
Isoquant analysis
Deriving an LRAC curve from an isoquant map
Units of capital (K)
Deriving an LRAC curve from an isoquant map
At an output of 200 LRAC = TC2 / 200
100 200 1
2 TC
TC
O
Units of labour (L)
Deriving an LRAC curve from an isoquant map
Units of capital (K)
Note: increasing returns to scale up to 400 units; decreasing returns to scale above 400 units
700
100 200
TC 7
6 TC
Units of labour (L)
5 TC
2
4
TC
1
TC 3 TC
TC
O
600 500 400 300
Units of capital (K)
Deriving an LRAC curve from an isoquant map
Expansion path
700
100 200
TC 7
6 TC
Units of labour (L)
5 TC
2
4
TC
1
TC 3 TC
TC
O
600 500 400 300
Isoquant analysis
Deriving short-run costs from an isoquant map
Deriving short-run costs from an isoquant map
Units of capital (K)
The long-run situation: both factors variable
300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Deriving short-run costs from an isoquant map The long-run situation: both factors variable Units of capital (K)
Expansion path
300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Deriving short-run costs from an isoquant map
Units of capital (K)
The short-run situation: capital fixed in supply Expansion path
K1 300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300 TC = £60 000 TC = £20 000
O
TC = £40 000
200 100
L1
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300
TC = £22 000 TC = £20 000
O
L2
TC = £60 000 TC = £40 000
200 100
L1
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300
TC = £22 000 TC = £20 000
O
L2
L1
TC = £60 000
TC = £65 000
TC = £40 000
200 100 L3
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path bL
K2
bS
a
K1
300
TC = £22 000 TC = £20 000
O
L2
L1
TC = £60 000
TC = £65 000
TC = £40 000
200 100
L4
L3
Units of labour (L)
Isoquant analysis
Constructing isoquants
An isoquant
45 40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
b
20 15 10 5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
An isoquant
45
a
40
Units of K 40 20 10 6 4
Units of capital (K)
35 30 25
Units of L 5 12 20 30 50
Point on diagram a b c d e
b
20 15
c
10
d
e
5 0 0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
Isoquant analysis
Diminishing marginal rate of substitution
Diminishing marginal rate of factor substitution 14
g
Units of capital (K)
12 ∆K = 2
MRS = ∆K / ∆L
MRS = 2 h
10 ∆L = 1
8 6 4 2
isoquant
0 0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Diminishing marginal rate of factor substitution 14
g
Units of capital (K)
12 ∆K = 2
MRS = ∆K / ∆L
MRS = 2 h
10 ∆L = 1
8
j
MRS = 1 k
∆K = 1
6
∆L = 1
4 2
isoquant
0 0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Isoquant analysis
An isoquant map
An isoquant map
Units of capital (K)
30
20
10
I5 I1
0 0
10
Units of labour (L)
I2 20
I3
I4
Isoquant analysis
Returns to scale
Constant returns to scale
4
Units of capital (K)
R c
3
b
2
500
400
a
1
600
300 200
0 0
1
2
Units of labour (L)
3
Increasing returns to scale (beyond point b)
4
Units of capital (K)
R c
3
700 600
b
2
500 400
a
1
300 200
0 0
1
2
Units of labour (L)
3
Decreasing returns to scale (beyond point b)
4
Units of capital (K)
R c
3
500
b
2
400
a
1
300 200
0 0
1
2
Units of labour (L)
3
Isoquant analysis
Isocosts
An isocost
30
Assumptions
Units of capital (K)
25
PK = £20 000 W = £10 000 TC = £300 000
20
15
10
5
0 0
5
10
15
20
25
Units of labour (L)
30
35
40
An isocost
30
Assumptions
Units of capital (K)
25
PK = £20 000 W = £10 000 TC = £300 000
20
a
15
b
10
c
5
TC = £300 000 d
0 0
5
10
15
20
25
Units of labour (L)
30
35
40
Isoquant analysis
The least-cost method of production
Finding the least-cost method of production 35
Assumptions
Units of capital (K)
30
PK = £20 000 W = £10 000
25
TC = £200 000 TC = £300 000
20 15
TC = £400 000 10
TC = £500 000
5 0 0
10
20
30
Units of labour (L)
40
50
Finding the least-cost method of production 35
Units of capital (K)
30 25
s
TC = £500 000
20 15
TC = £400 000
r
10
t
5
TPP1
0 0
10
20
30
Units of labour (L)
40
50
Isoquant analysis
Effect of a rise in the wage rate
Effect of a wage rise on the least-cost method of production 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000
25 20 15
TC = £400 000 10
r
8 5
TPP1 0 0
10
20
24
30
Units of labour (L)
40
50
Effect of a wage rise on the least-cost method of production (wage rises to £20 000) 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000 = £20 000
25 20 15
TC = £400 000 10
r
8 5
TPP1 0 0
10
20
24
30
Units of labour (L)
40
50
Effect of a wage rise on the least-cost method of production (wage rises to £20 000) 35
Units of capital (K)
30
Assumptions PK = £20 000 W = £10 000 = £20 000
25 20 15
TC = £400 000
r
1
10 1
r
8 5
TPP1 0 0
910
20
24
30
Units of labour (L)
40
50
Isoquant analysis
The maximum output for a given cost
Units of capital (K)
Finding the maximum output for a given total cost
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Units of capital (K)
Finding the maximum output for a given total cost
Isocost
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Finding the maximum output for a given total cost r Units of capital (K)
s
u v
TPP5 TPP4 TPP3 TPP2
TPP1
O Units of labour (L)
Finding the maximum output for a given total cost r Units of capital (K)
s
K1
t
u v O
TPP5 TPP4 TPP3 TPP2
TPP1 L1 Units of labour (L)
Isoquant analysis
Deriving an LRAC curve from an isoquant map
Units of capital (K)
Deriving an LRAC curve from an isoquant map
At an output of 200 LRAC = TC2 / 200
100 200 1
2 TC
TC
O
Units of labour (L)
Deriving an LRAC curve from an isoquant map
Units of capital (K)
Note: increasing returns to scale up to 400 units; decreasing returns to scale above 400 units
700
100 200
TC 7
6 TC
Units of labour (L)
5 TC
2
4
TC
1
TC 3 TC
TC
O
600 500 400 300
Units of capital (K)
Deriving an LRAC curve from an isoquant map
Expansion path
700
100 200
TC 7
6 TC
Units of labour (L)
5 TC
2
4
TC
1
TC 3 TC
TC
O
600 500 400 300
Isoquant analysis
Deriving short-run costs from an isoquant map
Deriving short-run costs from an isoquant map
Units of capital (K)
The long-run situation: both factors variable
300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Deriving short-run costs from an isoquant map The long-run situation: both factors variable Units of capital (K)
Expansion path
300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Deriving short-run costs from an isoquant map
Units of capital (K)
The short-run situation: capital fixed in supply Expansion path
K1 300 TC = £60 000 TC = £20 000
TC = £40 000
200 100
O Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300 TC = £60 000 TC = £20 000
O
TC = £40 000
200 100
L1
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300
TC = £22 000 TC = £20 000
O
L2
TC = £60 000 TC = £40 000
200 100
L1
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path
K1 300
TC = £22 000 TC = £20 000
O
L2
L1
TC = £60 000
TC = £65 000
TC = £40 000
200 100 L3
Units of labour (L)
Units of capital (K)
Deriving short-run costs from an isoquant map
Expansion path bL
K2
bS
a
K1
300
TC = £22 000 TC = £20 000
O
L2
L1
TC = £60 000
TC = £65 000
TC = £40 000
200 100
L4
L3
Units of labour (L)
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