The Firm s Short-Run Supply. Decision

Transcription

1 The Short-Run The short-run is a period of time in which at least one of the firm s inputs is fixed (as a result of previous decisions). For example, the lease on land ma be for one ear, in which case the monthl decisions of the firm must treat the amount of this input (land) as fixed. Suppose input 2 is fixed in the short run while input 1 is variable. Deriving the short-run cost (when there are 2 inputs) is an eas exercise. Suppose input 2 is fixed at level x 2. Then corresponding to an there is a unique level x 1 such that f(x 1, x 2 )=. The short run cost, c s (, x 2 ) can now be written simpl as c s (, x 2 )= w 1 x 1 + w 2 x 2 where f(x 1, x 2 )=. Note that there is a short-run cost function corresponding to each level at which the input is fixed. Given w 1, w 2 there is onl one long-run cost function. But there are man short-run cost functions, one for ever level at which the fixed input is fixed.

2 The Firm s Short-Run Suppl Decision p e MC s () s *

3 The Firm s Short-Run Suppl Decision At = s *, p = MC and MC slopes upwards. = s * is profit-maximizing. p e MC s () s *

4 The Firm s Short-Run Suppl Decision At = s *, p = MC and MC slopes upwards. = s * is profit-maximizing. p e MC s () s * At =, p = MC and MC slopes downwards. = is profit-minimizing.

5 The Firm s Short-Run Suppl p e Decision At = s *, p = MC and MC slopes upwards. = s * is profit-maximizing. So a profit-max. suppl level MC s () s * can lie onl on the upwards sloping part of the firm s MC curve.

6 The Firm s Short-Run Suppl Decision But not ever point on the upwardsloping part of the firm s MC curve represents a profit-maximum. The firm s profit function is ( ) = p c ( ) = p F c ( ). Π s s v If the firm chooses = 0 then its profit is Π s ( ) = 0 F c ( 0) = F. v

7 The Firm s Short-Run Suppl Decision So the firm will choose an output level > 0 onl if ( ) = p F c ( ) F. Π s I.e., onl if v p c ( ) 0 v Equivalentl, onl if p c v ( ) = AVC s ( ).

8 The Firm s Short-Run Suppl Decision MC s () AC s () AVC s ()

9 The Firm s Short-Run Suppl Decision MC s () AC s () AVC s ()

10 The Firm s Short-Run Suppl Decision p > AVC s () s * > 0. MC s () AC s () AVC s () p < AVC s () s * = 0.

11 The Firm s Short-Run Suppl Decision p > AVC s () s * > 0. MC s () AC s () AVC s () The firm s short-run suppl curve p < AVC s () s * = 0.

12 The Firm s Short-Run Suppl Decision Shutdown point MC s () AC s () AVC s () The firm s short-run suppl curve

13 The Firm s Short-Run Suppl Decision Shut-down is not the same as exit. Shutting-down means producing no output (but the firm is still in the industr and suffers its fixed cost). Exiting means leaving the industr, which the firm can do onl in the long-run.

14 There must be a relationship between short-run and long-run costs. Suppose we consider the short run in which x 2 = x 2 (ȳ). Then c s (ȳ, x 2 )=c(ȳ) and c s (, x 2 ) c() for all. The first equalit states that at output level ȳ, at which the firm would have chosen x 2 if it had a choice, the short-run cost is equal to the long-run cost. The second condition states that at other levels of output the short-run cost must be at least as high as the long-run cost; in general it will be higher. Thus c s (, x 2 ) will generall lie above c(), and the two curves will be tangent to each other at = ȳ. Of course, at ȳ the shortrun total, average and marginal cost must equal the long-run total, average and marginal cost, respectivel.

15 The Firm s Long & Short-Run Suppl Decisions AC s () MC() MC s () AC()

16 The Firm s Long & Short-Run Suppl Decisions AC s () MC() p MC s () AC() s * * s * is profit-maximizing in this short-run.

17 The Firm s Long & Short-Run Suppl Decisions AC s () MC() p Π s MC s () AC() s * * s * is profit-maximizing in this short-run.

18 The Firm s Long & Short-Run Suppl Decisions AC s () MC() p MC s () Π s Π" AC() s * * The firm can increase profit b increasing x 2 and producing * output units.

19 The Firm s Long & Short-Run Suppl Decisions AC s () MC() MC s () AC() p s * s * is loss-minimizing in this short-run.

20 The Firm s Long & Short-Run Suppl Decisions AC s () MC() MC s () AC() p Loss s * s * is loss-minimizing in this short-run.

21 The Firm s Long & Short-Run Suppl Decisions AC s () MC() MC s () AC() p Loss s * This loss can be eliminated in the long run b the firm exiting the industr.

22 The Firm s Long & Short-Run Suppl Decisions MC() AC()

23 The Firm s Long & Short-Run Suppl Decisions MC() AC()

24 The Firm s Long & Short-Run Suppl Decisions MC() AC()

25 The Firm s Long & Short-Run Suppl Decisions Long-run suppl curve MC() AC() Short-run suppl curves

26 Producer s Surplus The firm s producer s surplus is the accumulation, unit b extra unit of output, of extra revenue less extra production cost. How is producer s surplus related profit?

27 Producer s Surplus MC s () p AC s () AVC s () c v ( * (p)) = *( p) 0 MC s (z)d(z) *(p)

28 Producer s Surplus MC s () p Revenue = p*(p) AC s () AVC s () *(p)

29 Producer s Surplus MC s () p Revenue = p*(p) c v (*(p)) AC s () AVC s () *(p)

30 Producer s Surplus MC s () p PS AC s () AVC s () *(p)

31 Producer s Surplus The firm s producer s surplus is *( p) PS( p) = [ p MC ( z) ] d( z) 0 = p* ( p) MC ( z) d( z) = p* ( p) c * ( p). s *( p) v 0 s ( ) That is, PS = Revenue - Variable Cost.

32 Producer s Surplus PS = Revenue - Variable Cost. Profit = Revenue - Total Cost = Revenue - Fixed Cost - Variable Cost. So, PS = Profit + Fixed Cost. Onl if fixed cost is zero (the long-run) are PS and profit the same.