Isoquant Analysis Isoquant Analysis
Isoquant Analysis
Jan 03, 2016
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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