topic 6 : production and cost. k l q 100 0 0 100 1 10 100 2 25 100 3 45 100 4 70 100 5 90 100 6 100...
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Topic 6 : Production and Cost
K L Q 100 0 0 100 1 10 100 2 25
100 3 45 100 4 70 100 5 90 100 6 100 100 7 102
The Production Process(Short Run)
70
2545
10090
102
Q
L0 1 2 3 4 5 6 7
10
Q
L0 1 2 3 4 5 6 7
The Total Product (TP)Curve
25
1520
Q
L0 1 2 3 4 5 6 7
1020
10 2
Diminishing Returns to Labour set in from the 5th unit onwards
Q
L0 1 2 3 4 5 6 7
The MarginalProduct (MP)Curve
2515
20
Q
L0 1 2 3 4 5 6 7
1020
10
MP
AP
Q
L0 1 2 3 4 5 6 7
AP
MP
If MP > AP, then AP is rising
If MP < AP, then AP is falling
If MP = AP, then AP is stationary
From Production to Cost
MC = W/MP
where W is a fixed and known wage rate
£
0 1 2 3 4 5 6 7Q
MC
AVC
£
0 1 2 3 4 5 6 7Q
MC
AVC
£
0 1 2 3 4 5 6 7Q
MC
AVC
If MC < AVC, then AVC is falling
If MC > AVC, then AVC is rising
If MC = AVC, then AVC is stationary
£
Q0 1 2 3 4 5 6 7
.
.
..
. ..AFC
The graph of AFC
£
Q0 1 2 3 4 5 6 7
.
.
..
. ..AFCAVC
.
..
.
. . .ATC
£
Q0 1 2 3 4 5 6 7
AVC
.
..
.
. . .ATCMC
£
0 1 2 3 4 5 6 7Q
MC ATC
If MC < ATC, then ATC is falling
If MC > ATC, then ATC is rising
If MC = ATC, then ATC is stationary
The Short Run Average Cost(SAC) for a given value of Capital (K = K*)
Q
£
O
SAC
SAC1 SAC4SAC3
SAC2
Q
£
O
O Q
£ The Long Run Average Cost (LAC) envelopes the SAC curves
LAC
O Q
£
LMC LAC
SMC1 SMC2 SMC3SMC4
Construction of the LMC
An isoquant is the path joining points in the L-K space that represent input combinations that produce the same amount of output
It is derived from the long run production function by fixing the output level.
It is a concept similar to that of an indifference curve introduced earlier.
The Production Process(Long Run)
The isoquants are drawn downward sloping as long as inputs have a positive marginal product.
That is, the isoquants must slope downwards if adding a factor of production (holding the other factor constant) adds to output.
Question: How would the isoquants shape if some factor (say L) has a negative marginal product?
These curves are drawn convex to the origin to reflect DIMINISHING MRTSKL .
As more L is used to substitute, it becomes increasingly more difficult to substitute K by L.
lo
k
10
20
30
A
C
B
OA=AB= BC
Constant Returns to Scale
lo
k
10
20A
C
B
OA=AB= BC
Decreasing Returns to Scale
lo
k
1020
A
C
B
OA=AB= BC
Increasing Returns to Scale
lo
k
1 23
4
100 240180
Expansion Path(Long Run)
Q
£
O
100
180
240
1 2 3
Long Run TotalCost (LTC)
Q
£
O
100 90
1 2 3
Long Run AverageCost (LAC) andLong Run Marginal Cost(LMC)
80
LAC
LMC 60
O Q
£
LMC LACSMCSAC
Q*
At Q*, SMC = LMC
At Q > Q*, SMC > LMC
At Q < Q*, SMC < LMC
lo
k
1
3
2
100
200
280
340120
Expansion Path(Long Run)
Expansion Path(Short Run)
At Q > Q*,SMC > LMC
LMC of 1st unit= (200-100) = 100
SMC of 3rd unit= (340-200) = 140
LMC of 3rd unit= (280-200) = 80
SMC of 1st unit= (200-140) = 60
At Q < Q*,SMC < LMC
Decreasing Returns to Scale (DRS) and Diminishing Returns to a Factor (DRF)• DRS is a long run concept so that all
factors are changeable.
• DRF is a short–run concept, with the existence of fixed factors of production.
• Does DRS imply DRF?
K L Q
1 1 1
3 3 2
Instead, suppose we fix K at 1 and only treble L.
If K has a positive marginal productivity, Q will be less than 2.
This production process exhibits DRS
DRS implies DRF
EXAMPLE 1Short Run Production (K is fixed at 1) L Q 1 2 2 3Long Run Production (K is variable) L K Q 1 1 2 2 2 6
EXAMPLE 2Short Run Production function (K is
fixed at 1)L Q1 22 3Long Run Production (K is variable) L K Q 1 1 2 2 2 3.5
• The first of the two numerical examples shows that DRF may not always lead to DRS;
• the second shows that DRF may sometimes lead to DRS.
DRF does not necessarily imply DRS