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Topic 6 : Production and Cost
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The Production Process
(Short Run) K L Q
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Q 102 100 90 70 45 25 10 L
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Q The Total Product (TP) Curve L
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Diminishing Returns to Labour set in from the 5th unit onwards
Q Diminishing Returns to Labour set in from the 5th unit onwards 25 20 20 15 10 10 2 L
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Q The Marginal Product (MP) Curve L
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AP Q MP 20 25 20 15 10 10 L
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If MP > AP, then AP is rising
Q If MP < AP, then AP is falling If MP = AP, then AP is stationary AP MP L
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From Production to Cost where W is a fixed and known
MC = W/MP where W is a fixed and known wage rate
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MC AVC Q
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MC AVC Q
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If MC < AVC, then AVC is falling
If MC > AVC, then AVC is rising If MC = AVC, then AVC is stationary MC AVC Q
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. The graph of AFC . . . . . . AFC Q
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. . . . . . . . . . ATC . . . AVC . AFC Q
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. . . . . MC . . ATC AVC Q
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If MC < ATC, then ATC is falling
If MC > ATC, then ATC is rising If MC = ATC, then ATC is stationary MC ATC Q
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The Short Run Average Cost (SAC) for a given value of Capital (K = K*) SAC Q O
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SAC2 SAC1 SAC4 SAC3 Q O
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The Long Run Average Cost (LAC) envelopes the SAC curves
The Long Run Average Cost (LAC) envelopes the SAC curves LAC Q O
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Construction of the LMC
SMC4 SMC3 SMC1 SMC2 LMC LAC Q O
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The Production Process
(Long Run) 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.
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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?
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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.
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Constant Returns to Scale
OA=AB= BC k C 30 B A 20 10 o l Constant Returns to Scale
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Decreasing Returns to Scale
OA=AB= BC k C B A 20 10 o l Decreasing Returns to Scale
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Increasing Returns to Scale
OA=AB= BC k C B A 20 10 o l Increasing Returns to Scale
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Expansion Path (Long Run) k 4 3 2 1 o l 180 240 100
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Long Run Total Cost (LTC) 240 180 100 O Q 1 2 3
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Long Run Average Cost (LAC) and Marginal Cost (LMC) 100 LAC 90 80 60 LMC Q 1 2 3 O
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At Q < Q*, SMC < LMC At Q*, SMC = LMC SAC SMC LMC LAC Q* Q O At Q > Q*, SMC > LMC
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280 200 Expansion Path (Long Run) Expansion Path 100 3 (Short Run) 1 2
k 280 200 Expansion Path (Long Run) Expansion Path (Short Run) 100 3 1 2 o l 340 120
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SMC of 3rd unit = ( ) = 140 LMC of 3rd unit = ( ) = 80 At Q > Q*,SMC > LMC LMC of 1st unit = ( ) = 100 SMC of 1st unit = ( ) = 60 At Q < Q*, SMC < LMC
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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?
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Instead, suppose we fix K at 1 and only treble L.
K L Q 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
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EXAMPLE 1 Short Run Production (K is fixed at 1) L Q Long Run Production (K is variable) L K Q
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EXAMPLE 2 Short Run Production function (K is fixed at 1) L Q 1 2 2 3 Long Run Production (K is variable) L K Q
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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
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