Topic 6 : Production and Cost

The Production Process (Short Run) 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

Q 102 100 90 70 45 25 10 L 0 1 2 3 4 5 6 7

Q The Total Product (TP) Curve L 0 1 2 3 4 5 6 7

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 0 1 2 3 4 5 6 7

Q The Marginal Product (MP) Curve L 0 1 2 3 4 5 6 7

AP Q MP 20 25 20 15 10 10 L 0 1 2 3 4 5 6 7

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 0 1 2 3 4 5 6 7

From Production to Cost where W is a fixed and known MC = W/MP where W is a fixed and known wage rate

MC £ AVC Q 0 1 2 3 4 5 6 7

MC £ AVC Q 0 1 2 3 4 5 6 7

If MC < AVC, then AVC is falling £ If MC > AVC, then AVC is rising If MC = AVC, then AVC is stationary MC AVC Q 0 1 2 3 4 5 6 7

£ . The graph of AFC . . . . . . AFC Q 0 1 2 3 4 5 6 7

. £ . . . . . . . . . ATC . . . AVC . AFC Q 0 1 2 3 4 5 6 7

. £ . . . . MC . . ATC AVC Q 0 1 2 3 4 5 6 7

If MC < ATC, then ATC is falling £ If MC > ATC, then ATC is rising If MC = ATC, then ATC is stationary MC ATC Q 0 1 2 3 4 5 6 7

£ The Short Run Average Cost (SAC) for a given value of Capital (K = K*) SAC Q O

£ SAC2 SAC1 SAC4 SAC3 Q O

The Long Run Average Cost (LAC) envelopes the SAC curves £ The Long Run Average Cost (LAC) envelopes the SAC curves LAC Q O

Construction of the LMC £ SMC4 SMC3 SMC1 SMC2 LMC LAC Q O

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.

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.

Constant Returns to Scale OA=AB= BC k C 30 B A 20 10 o l Constant Returns to Scale

Decreasing Returns to Scale OA=AB= BC k C B A 20 10 o l Decreasing Returns to Scale

Increasing Returns to Scale OA=AB= BC k C B A 20 10 o l Increasing Returns to Scale

Expansion Path (Long Run) k 4 3 2 1 o l 180 240 100

£ Long Run Total Cost (LTC) 240 180 100 O Q 1 2 3

Long Run Average Cost (LAC) and Marginal Cost (LMC) £ 100 LAC 90 80 60 LMC Q 1 2 3 O

At Q < Q*, SMC < LMC £ At Q*, SMC = LMC SAC SMC LMC LAC Q* Q O At Q > Q*, SMC > LMC

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

SMC of 3rd unit = (340-200) = 140 LMC of 3rd unit = (280-200) = 80 At Q > Q*,SMC > LMC LMC of 1st unit = (200-100) = 100 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?

Instead, suppose we fix K at 1 and only treble L. 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 1 Short Run Production (K is fixed at 1)  L Q 1 2 2 3 Long Run Production (K is variable)  L K Q   1 1 2 2 2 6

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  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