simba nyakdee nyakudanga presentation on isoquants
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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’
• -’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’
• -’Quant’ as in quantity
• Isoquant – a line of equal quantity
Unitsof K402010 6 4
Unitsof L 512203050
Point ondiagram
abcde
a
Units of labour (L)
Un
its o
f ca
pita
l (K
)An isoquant yielding output (TPP) of 5000 unitsAn isoquant yielding output (TPP) of 5000 units
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
)
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
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
)
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 (technical)
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 (technical)
substitution
– Rate at which we can substitute capital for
labour and still maintain output at the given
level. MRTS = K / L
Sometimes just called Marginal rate of Substitution (MRS)
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
MRTS = -2 MRTS = K / L
Diminishing marginal rate of tech. substitutionDiminishing marginal rate of tech. 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
Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution
isoquant
MRTS = -2
MRTS = -1
MRTS = K / L
0
10
20
30
0 10 20
An isoquant mapAn isoquant mapU
nits
of c
ap
ital (
K)
Units of labour (L)
Q1=5000
0
10
20
30
0 10 20
Q2=7000
Un
its o
f ca
pita
l (K
)
Units of labour (L)
An isoquant mapAn isoquant map
Q1
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
An isoquant mapAn isoquant map
Q1Q2
Q3
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
An isoquant mapAn isoquant map
Q1Q2
Q3
Q4
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
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
• E.g: Cobb-Douglas Production Function
Q=K1/2 L1/2
• We now turn to an important aspect of
production, namely returns to scale.
• Isoquants
• E.g: Cobb-Douglas Production Function
Q=K1/2 L1/2
• We now turn to an important aspect of
production, namely 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
Suppose producing 5000 units with 10 units of capital and 5 units of
labour
What happens now if we double
the amount of capital and
labour?
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Suppose producing 5000 units with 10 units of capital and 5 units of
labour
What happens now if we double
the amount of capital and
labour?
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
What is the output level at this new isoquant?
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Suppose 20 K and 10 L gives 10,000 units
then we say there are constant 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 Q(2K,2L)
= 2Q(K,L) =10,000
Q2=10,000
Constant Returns to ScaleConstant Returns to Scale
• For example the Cobb-Douglas Production For example the Cobb-Douglas Production Function: Q(K,L)= Function: Q(K,L)= K1/2 L1/2
Q(2K,2L)= (2Q(2K,2L)= (2K)1/2(2L)1/2
=2 =2 K1/2L1/2 =2Q(K,L)Q(K,L)
A function such that Q(aK,aL)=aQ(K,L) for all A function such that Q(aK,aL)=aQ(K,L) for all a>0 (or a=0), is said to be HOMOGENOUS a>0 (or a=0), is said to be HOMOGENOUS OF DEGREE 1 (sometimes: LINEAR OF DEGREE 1 (sometimes: LINEAR HOMOGENOUS) HOMOGENOUS)
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
and Q(2K,2L)=15,000
>2Q(K,L)=10000
Then there is IRSQ2=15,000
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
Increasing returns to scale:
“Isoquants get closer together”
Q2=15,000
Q2=10,000
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
and
Q(2K,2L)=7,000
< 2Q(K,L)=10000Q2=7,000
Decreasing returns to scale, DRS
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Q2=7,000
Q2=10,000
Decreasing returns to scale: “Isoquants get further apart”
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5
Q2=7,000
Q2=10,000
If Decreasing returns to scale: “Isoquants get further apart”
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
– isoquants and marginal returns:
The Marginal Return measures the change in
output when one variable is changed and the
other is kept fixed.
– 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:
The Marginal Return measures the change in
output when one variable is changed and the
other is kept fixed.
– 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
• Next, holding capital constant at K=20 we
examine the different amounts of labour
required to produce
• 5000, 10,000, and 15,000 units of output
• Next, holding capital constant at K=20 we
examine the different amounts of labour
required to produce
• 5000, 10,000, and 15,000 units of output
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q1=10,000
Q3=15000
232
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q1=10,000
Q3=15000With K
Constant, Q1 to Q2 requires 8 L
232
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q1=10,000
Q3=15000With K
Constant, Q1 to Q2 requires 8 L
With K Constant, Q2 to Q3 requires 13 L
2 23
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• So 5000 to 10,000 requires 8 extra L
• 10,000 to 15,000 requires 13 extra L
• So 5000 to 10,000 requires 8 extra L
• 10,000 to 15,000 requires 13 extra L
0
10
20
30
0 10 20
Un
its o
f ca
pita
l (K
)
Units of labour (L)
Q1=5000
5 15
Q1=10,000
Q3=15000
<- 8 L -> <- 13 L ->
2 23
What principle is this?
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• So 5000 to 10,000 requires 8 extra L
• 10,000 to 15,000 requires 13 extra L
• What principle is this?
• So 5000 to 10,000 requires 8 extra L
• 10,000 to 15,000 requires 13 extra L
• What principle is this?
•Principle of Diminishing MARGINAL
returns
•Note: So CRS and diminishing marginal
returns go well together
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Isoquants
– their shape
– diminishing marginal rate of substitution
– isoquants and returns to scale
– isoquants and marginal returns
• Isoquants
– their shape
– diminishing marginal rate of substitution
– isoquants and returns to scale
– isoquants and marginal returns
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• We now add the firms’ costs to the analysis !
• Suppose bank or venture Capitalist will only lend
you £300,000
• How much capital and labour can you buy / hire?
• ISOCOST- Line of indicating set of inputs with
‘equal’ Cost
• We now add the firms’ costs to the analysis !
• Suppose bank or venture Capitalist will only lend
you £300,000
• How much capital and labour can you buy / hire?
• ISOCOST- Line of indicating set of inputs with
‘equal’ Cost
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
An isocostAn isocost
Units of labour (L)
Un
its o
f ca
pita
l (K
)
Assumptions
PK = £20 000 W = £10 000
TC = £300 000
a
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
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
)
a
b
c
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
TC = WL + PKK
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40 45 50 55 60
Units of labour (L)
Un
its o
f ca
pita
l (K
)
Assumptions
PK = £20 000 W = £5,000
TC = £300 000
Suppose Price of Labour (wages) fallsSuppose Price of Labour (wages) falls
TC = £300 000
Slope of Line =
-W/PK
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40 45 50 55 60
Units of labour (L)
Un
its o
f ca
pita
l (K
)
TC = £500 000
Assumptions
PK = £20 000 W = £10 000
TC = £500 000
Suppose Bank increases Finance to £500,000Suppose Bank increases Finance to £500,000
TC = £300 000
NOTE!NOTE!
ISOQUANT and ISOCOST CURVES hopefully ISOQUANT and ISOCOST CURVES hopefully remind you a lot about INDIFFERENCE remind you a lot about INDIFFERENCE CURVES and BUDGET LINES...CURVES and BUDGET LINES...
Efficient production:Efficient production:
• Two types of problems:
• 1. Least-cost-combination of factors for a given output level
• Two types of problems:
• 1. Least-cost-combination of factors for a given output level
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Finding the least-cost method of productionFinding the least-cost method of production
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
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
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
TPP1
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
TC = £400 000r
TPP1
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
TC = £400 000
TC = £500 000s
r
tTPP1
ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS
• Least-cost-combination of factors for a given output level
– Produce on lowest isocost line where the iosquant just touches it at a point of tangency
– We’ll get back to this !
• Least-cost-combination of factors for a given output level
– Produce on lowest isocost line where the iosquant just touches it at a point of tangency
– We’ll get back to this !
Efficient production:Efficient production:
• Effectively have two types of problem
• 1. Least-cost combination of factors for a given output
• 2. Highest output for given production costs
• 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 given production costs
• Here have Financial Constraint:
E.g.: Venture Capital
Finding the maximum output for given total costsFinding the maximum output for given total costs
Q1Q2
Q3
Q4
Q5
Un
its o
f ca
pita
l (K
)
Units of labour (L)
O
O
Isocost
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP1TPP2
TPP3
TPP4
TPP5
Finding the maximum output for given total costsFinding the maximum output for given total costs
O
r
v
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP1TPP2
TPP3
TPP4
TPP5
Finding the maximum output for given total costsFinding the maximum output for given total costs
O
s
u
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP1TPP2
TPP3
TPP4
TPP5
r
v
Finding the maximum output for given total costsFinding the maximum output for given total costs
O
t
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP1TPP2
TPP3
TPP4
TPP5
r
v
s
u
Finding the maximum output for given total costsFinding the maximum output for given total costs
O
K1
L1
Un
its o
f ca
pita
l (K
)
Units of labour (L)
TPP1TPP2
TPP3
TPP4
TPP5
r
v
s
u
t
Finding the maximum output for given total costsFinding the maximum output for given total costs
Efficient production:Efficient production:
• 1. Least-cost combination of factors for a given output
• 2. Highest output for a given cost of production
• Comparison with Marginal Product Approach
• 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 =-MPPKdK
Gain of Output if increase L =MPPLdL
Along an Isoquant dQ=0 so -MPPKdK =MPPLdL
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
MRTS = dK / dL
Recall Recall MRTS = dK / dL
Along an Isoquant dQ=0 so -MPPKdK =MPPLdL
K
L
MPP
MPP
dL
dK
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
MRTS = dK / dL
Recall Recall MRTS = dK / dL
Along an Isoquant dQ=0 so -MPPKdK =MPPLdL
K
L
MPP
MPP
dL
dKMRTS
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 = - PKdK
Rise in cost if increase L = PLdL
Along an isocost line
-PKdK = PLdL
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?
Along an isocost line
-PKdK = PL dL
K
L
P
P
dL
dK
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
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
K
K
L
L
P
MPP
P
MPP
• 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
• Then extra output per £1 spent on labour greater than extra output per £1 spent on Then extra output per £1 spent on labour greater than extra output per £1 spent on CapitalCapital
• So switch resources from Capital to LabourSo switch resources from Capital to Labour• MPPMPPLL??
– DownDown
• MPPMPPKK? ? – UpUp
(Principle of Diminishing Marginal Returns)(Principle of Diminishing Marginal Returns)
K
K
L
L
P
MPP
P
MPP
K
K
L
L
P
MPP
P
MPPSuppose
LONG-RUN COSTSLONG-RUN COSTS
• Derivation of long-run costs from an isoquant map
– derivation of long-run costs
• Derivation of long-run costs from an isoquant map
– derivation of long-run costs
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
Deriving an Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
TC1
100
At an output of 100LRAC = TC1 / 100
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
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100300
400500
600
700
Deriving an Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
Are the Isoquants getting closer or
further apart here?
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100300
400500
600
700
Deriving an Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
Getting Closer up to 400, getting further
apart after 400
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100300
400500
600
700
Deriving an Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
What does that mean?
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 Deriving an LRACLRAC curve from an isoquant map curve from an isoquant map
LONG-RUN COSTSLONG-RUN COSTS
• Derivation of long-run costs from an isoquant map
– derivation of long-run costs
– the expansion path
• Derivation of long-run costs from an isoquant map
– derivation of long-run costs
– the expansion path
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 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
A typical long-run average cost curveA typical long-run average cost curve
OutputO
Co
sts
LRACEconomiesof scale
Constantcosts
Diseconomiesof scale
A typical long-run average cost curveA typical long-run average cost curve
OutputO
Co
sts
LRAC
MC
MC
What about the Short-RunWhat about the Short-Run
• Derivation of short-run costs from an isoquant map
– Recall in SR Capital stock is fixed
• Derivation of short-run costs from an isoquant map
– Recall in SR Capital stock is fixed
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 a SDeriving a SRACRAC curve from an isoquant map curve from an isoquant map
Suppose initially at Long-Run
Equilibrium at K0L0
L0
K0
What would happen if had to
produce at a different level?
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
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
To make life simple lets just focus on
two isoquants, 700 and 100
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100
400
700
Deriving a SDeriving a SRACRAC curve from an isoquant map curve from an isoquant map
Consider an output level such
as Q=700
Hold SR capital constant at K0
L0
K0
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100
400
700
Deriving a SDeriving a SRACRAC curve from an isoquant map curve from an isoquant map
Locate the cheapest production point in SR
on K0 line
L0
K0
TC in SR is obviously higher
than LR
Un
its o
f ca
pita
l (K
)
O
Units of labour (L)
TC1
TC2
TC3
TC4
TC5
TC6
TC7
100
400
700
Deriving a SDeriving a SRACRAC curve from an isoquant map curve from an isoquant map
Similarly, consider an output level such as Q=100
L0
K0
Again TC in SR is obviously higher
than LR
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
What about the Short-RunWhat about the Short-Run
• Derivation of short-run costs from an isoquant map
– Recall in SR Capital stock is fixed
• In SR TC is always higher than LR
• ….and Average costs?
• Derivation of short-run costs from an isoquant map
– Recall in SR Capital stock is fixed
• In SR TC is always higher than LR
• ….and Average costs?
A typical short-run average cost curveA typical short-run average cost curve
OutputO
Co
sts
LRACSRAC