Post on 25-Dec-2015
Chapter 5The Firm
And the Isoquant Map
Chapter 5The Firm
And the Isoquant Map
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquant
• A line indicating the level of inputs required
to produce a given level of output
• Iso- meaning - ‘Equal’
– As in ‘Iso’-bars
• -’Quant’ as in quantity
• Isoquant – a line of equal quantity
• Isoquant
• A line indicating the level of inputs required
to produce a given level of output
• Iso- meaning - ‘Equal’
– As in ‘Iso’-bars
• -’Quant’ as in quantity
• Isoquant – a line of equal quantity
Unitsof K402010 6 4
Unitsof L 512203050
Point ondiagram
abcde
a
b
Units of labour (L)
Un
its o
f ca
pita
l (K
)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
An isoquant yielding output (TPP) of 5000 unitsAn isoquant yielding output (TPP) of 5000 units
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
– their shape
– diminishing marginal rate of substitution
– Rate at which we can substitute capital for
labour and still maintain output at the given
level.
• Isoquants
– their shape
– diminishing marginal rate of substitution
– Rate at which we can substitute capital for
labour and still maintain output at the given
level.MRS = K / L
Sometimes called Marginal rate of Technical Substitution
MRTS = K / L
0
10
20
30
0 10 20
Q1Q2
Q3
Q4
Q5
Un
its o
f ca
pita
l (K
)
Units of labour (L)
An isoquant mapAn isoquant map
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
Then Q(2K,2L)
= 2Q(K,L) =10,000
Q2=10,000
Constant Returns to ScaleConstant Returns to Scale
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
Then IRS =>Q(2K,2L)=15,000
> 2Q(K,L)
Q2=15,000
If Increasing returns to scale, IRS
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
If Q(K,L) =5000
Then DRS=>
Q(2K,2L)=7,000
< 2Q(K,L)Q2=7,000
If Decreasing returns to scale, DRS
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
– isoquants and marginal returns:
– Marginal Returns means changing one variable
and keeping the other constant.
– To see this, suppose we examine the CRS
diagram again, this time with 3 isoquants,
– 5000, 10,000, and 15,000
• Isoquants
– isoquants and marginal returns:
– Marginal Returns means changing one variable
and keeping the other constant.
– To see this, suppose we examine the CRS
diagram again, this time with 3 isoquants,
– 5000, 10,000, and 15,000
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q2=10,000
Q3=15000
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
– their shape
– diminishing marginal rate of substitution
– isoquants and returns to scale
– isoquants and marginal returns
• Isoquants- focussing on issue of efficient
way to produce
– E.g. Supply Tesco’s with Yogurt
• Isoquants
– their shape
– diminishing marginal rate of substitution
– isoquants and returns to scale
– isoquants and marginal returns
• Isoquants- focussing on issue of efficient
way to produce
– E.g. Supply Tesco’s with Yogurt
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Other focus might be on Costs:
• Suppose bank or venture Capitalist will only
lend you £300,000
• What capital and labour will that buy you?
• ISOCOST- Line of indicating set of inputs
that give ‘equal’ Cost
• Other focus might be on Costs:
• Suppose bank or venture Capitalist will only
lend you £300,000
• What capital and labour will that buy you?
• ISOCOST- Line of indicating set of inputs
that give ‘equal’ Cost
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
)
a
b
c
Assumptions
PK = £20 000 W = £10 000
TC = £300 000
An isocostAn isocost
Efficient production:Efficient production:
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• E.g: The supplying Tesco’s problem
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• E.g: The supplying Tesco’s problem
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
)Finding the least-cost method of productionFinding the least-cost method of production
Target Level = TPPTarget Level = TPP11
Efficient production:Efficient production:
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• 2. Highest output for a given cost of production
• . Here have Financial Constraint:
• . E.g.: Venture Capital
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• 2. Highest output for a given cost of production
• . Here have Financial Constraint:
• . E.g.: Venture Capital
Finding the maximum output for a given total costFinding the maximum output for a given total cost
Q1Q2
Q3
Q4
Q5
Un
its o
f ca
pita
l (K
)
Units of labour (L)
O
Efficient production:Efficient production:
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• 2. Highest output for a given cost of production
• Comparison with Marginal Product Approach
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• 2. Highest output for a given cost of production
• Comparison with Marginal Product Approach
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20 22
Un
its o
f ca
pita
l (K
)
Units of labour (L)
isoquant
MRS = dK / dL
Recall Recall MRTS = dK / dL
Loss of Output if reduce K
Gain of Output if increase L
Along an Isoquant dQ=0 so
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
)
What about the slope of an isocost line?What about the slope of an isocost line?
Reduction in cost if reduce K
Rise in cost if increase L =
Along an isocost line
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
In equilibrium slope of Isoquant = Slope of isocostIn equilibrium slope of Isoquant = Slope of isocost
100
K
L
K
L
P
P
MPP
MPP
dL
dKMRTS
• Intuition is that money spent on each factor Intuition is that money spent on each factor should, at the margin, yield the same should, at the margin, yield the same additional outputadditional output
• Suppose notSuppose not
K
K
L
L
P
MPP
P
MPP
K
K
L
L
P
MPP
P
MPP
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 Deriving an LRACLRAC curve from an isoquant map 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
Deriving an Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TC
Total costs for firm in Long -RunTotal costs for firm in Long -Run
MC = TC / Q=20/1=20
Q=1
TC=20
A typical long-run average cost curveA typical long-run average cost curve
OutputO
Co
sts
LRAC
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC4
TC7
100
400
700
Deriving a SDeriving a SRACRAC curve from an isoquant map curve from an isoquant map
Suppose initially at Long-Run
Equilibrium at K0L0
L0
K0
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
LRTC
Total costs for firm in the Short and Long -RunTotal costs for firm in the Short and Long -Run
SRTC
A typical short-run average cost curveA typical short-run average cost curve
OutputO
Co
sts
LRACSRAC