Firm and Industry Supply

Transcription

1 Firm and Industry Supply M. Utku Ünver Micro Theory Boston College M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 1 / 26

2 FIRM SUPPLY M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 2 / 26

3 Firm s Objective Output price p given (competitive output market, as well as competitive input markets) Profit of a firm: π(y) = Revenue - Cost = py c(y) Firm s profit maximization problem: max y π(y) π(y) y = 0 [py c(y)] y = 0 p MC (y ) = 0 If there are several output levels where p = MC, then we should consider the case where MC is upward sloping. If there are still several such levels, then we should compare the profits at each such level. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 3 / 26

4 Producer Surplus and Profit Recall firm s profit maximization problem max y π(y) = py c(y) = py c v (y) F [py c v (y) F ] y p c v (y) y F y }{{} =0 Maximizing profit is identical to maximizing = 0 = 0 Producer Surplus (PS(y))= py c v (y), because F y = 0. PS = Revenue - Variable Cost = Profit + Fixed Cost In the long run, typically F = 0 and π(y) = PS(y). M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 4 / 26

5 Graphical Depiction of Producer Surplus M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 5 / 26

6 Graphical Depiction of Producer Surplus M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 6 / 26

7 Graphical Depiction of Producer Surplus PS = Area between price line and marginal cost, up to the quantity. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 7 / 26

8 Example: MC (y i ) = p for each i = 1,..., 7 PS(y 1 ) = A; PS(y 2 ) = A B; PS(y 3 ) = A B + C; PS(y 4 ) = A B + C D; PS(y 5 ) = A B + C D + E; PS(y 6 ) = A B + C D + E F ; PS(y 7 ) = A B + C D + E F + G; Thus, y 5 has the largest PS, so it maximizes profit as well... M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 8 / 26

9 Firm s Supply Curve in the Short Run : The firm shuts down (temporarily) when price falls so much that PS falls below 0 (as producing y = 0 gives PS(0) = 0) That happens when AVC is minimized: M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 9 / 26

10 Temporary Shut-Down Price Shut-down quantity y sd and price p sd are found when firm is maximizing PS, and despite this fact, the firm is indifferent between producing and not-producing, i.e., PS = 0, and if the price falls further down, PS < 0. 0 = PS(y sd ) = p sd y sd c v (y sd ) 0 = p sd y sd AVC (y sd )y sd = [p sd AVC (y sd )]y sd p sd = AVC (y sd ) PS max. says at p sd as the firm is producing y sd, p sd = MC (y sd ) Hence, p sd = AVC (y sd ) = MC (y sd ). (i.e., when AVC is minimized.) M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 10 / 26

11 INDUSTRY SUPPLY M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 11 / 26

12 Short Run vs Long Run In the short run, number of firms is fixed (i.e. there are fixed costs, thus no firm can freely enter or exit the market) In the long run, all inputs are freely changeable thus there are firms entering and exiting freely. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 12 / 26

13 Short-Run (Partial) Equilibrium Consider a single output market Short-run industry supply curve is horizontal sum of individual firms supply curves. Market demand curve is the horizontal sum of individuals demand curves. The price level that makes total quantity demanded = total quantity supplied is the equilibrium price and the quantity level is the equilibrium quantity. Since we assume other goods markets have prices fixed, this is known as the short-run partial competitive equilibrium. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 13 / 26

14 Now depending on the market demand we can find short-run eq.: N SR is given to us as the number of firms in the short run. So we can find (p SR, Y SR ), short-run equilibrium, and output per firm y SR = Y SR given that N SR firms exist in the market. N SR M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 14 / 26

15 Long-Run (Partial) Equilibrium Whenever economic profit= profit= revenue- cost > 0, it means that this market is more profitable (in monetary terms) than other industries. monetary profit- non-monetary opportunity cost= profit for economists. Profit=0 means that the industry is giving exactly monetary profit for the firm if it made business in the best alternative. Whenever, in the short-run equilibrium, there is profit> 0, new firms will enter the market in the long run. Whenever, in the short-run equilibrium, there is profit< 0, firms will exit the market in the long run. Thus, the long-run equilibrium will be determined at a price level where profit= 0 for each firm. Hence revenue - cost= 0. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 15 / 26

16 Hence revenue=cost p LR.y LR = AC (y LR ).y LR p LR = AC (y LR ) also we have p LR = MC (y LR ) for profit maximization, thus MC (y LR ) = AC (y LR ) Recall that marginal cost and average cost intersect at the minimum of average cost. Thus MC (y LR ) = AC (y LR ) gives us y LR, the long-run equilibrium firm production. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 16 / 26

17 Long-run equilibrium price p LR is the break-even price of the firms, corresponding output is the long-run equilibrium output y LR per firm. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 17 / 26

18 We need to figure out the number of firms by our-selves: New firms enter whenever short-run profit> 0, or exit if short-run profit< 0. Since firms enter and exit freely, any quantity can be supplied, at the price p LR. If there are identical firms, Long-Run Industry Supply Curve is a horizontal line at p LR M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 18 / 26

19 Example: There are 100 bakeries producing bread at a neighborhood with 10,000 households. Each household s demand curve is given by p = 5 y D, where y D refers to hundreds loaves of bread, and p is in dollars per loaf. Each bakery faces the same short-run and long-run cost c(y) = y (a) Find market demand curve, individual firm supply curve, and SR industry supply curve. (b) Find the SR equilibrium price and quantity per bakery and per household. (c) In the long run, new bakeries can freely enter/exit the market. What is the long-run equilibrium price? What is the LR industry supply curve? (d) Find the LR equilibrium quantity and number of bakeries. What is the quantity per household. (e) Find the new SR industry supply curve at the long-run equilibrium number of bakeries. M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 19 / 26

20 Solution: (a) Find market demand curve: p = 5 y D y D = 5 p Y D = 10, 000y D = 10, 000(5 p) (1) M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 20 / 26

21 Find individual firm and SR industry supply curves: c v (y) = y 2 MC (y) = c v (y) = 2y y AVC (y) = c v (y) = y (2) y Observe that supply follows MC (y) after MC (ỹ) = AVC (ỹ) where ỹ gives minimum variable cost, thus ỹ = 0 Individual firm supply curve is found as p = 2y SR Industry Supply is y = p 2 Y SR = N SR y = 100 p 2 = 50p M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 21 / 26

22 (b) At SR Equilibrium, markets clear, i.e., demand=supply, Y D = Y SR 10, 000(5 p) = 50p 50, 000 = 10, 050p p SR = Y SR = = (3) Each bakery: y SR = Y SR N = SR 100 = 2.49 Each household: y D,SR = ,000 = M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 22 / 26

23 (c) LR: Just find the LR price using the fact that LR profit=0, thus AC (y LR ) = MC (y LR ) = p LR AC (y) = c(y) y MC (y) = 2y = y + 4 y AC (y LR ) = MC (y LR ) y LR + 4 LR = 2y y LR (y LR ) 2 = 4 y LR = 2 p LR = y LR + 4 y LR = = 4 (4) M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 23 / 26

24 M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 24 / 26

25 (d) LR equilibrium quantity, find through demand: Market demand at p LR = 4 is Y D,LR = 10, 000(5 4) = 10, 000 Each household y D,LR = Y D,LR 10,000 = 1 unit of bread per year. supply=demand at LR equilibrium = Y LR = Y D,LR = 10, 000 There are N LR = Y LR = 10,000 y LR 2 = 5, 000 bakeries open 4,900 new bakeries are open in this neighborhood. (e) New short run is equivalent to the long run, however, we fix the number of bakeries at 5,000. With 5, 000 bakeries, new SR industry supply curve is Y SR = N LR y = 5, 0000 p 2 = 2, 500p M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 25 / 26

26 Question: Suppose that the real-estate agency market has 500 real-estate agencies at the long-run equilibrium and all have identical costs. Each agency supplies real-estate agents, which can be in multiple numbers. The market demand for real-estate agents is p = 10, 000 2y where y refers to the number of houses sold (equivalently, total number of agents employed, since one agent is employed for each sale) and p refers to the commission paid to the agencies per house sold. If the real-estate agency supply for the short run (of the same long run) has a constant slope 2, i.e. p = 2y and each agency faces the same unknown fixed cost, then find the cost function of each agency (hint: first find marginal cost of each agency, variable cost of each agency and then the long-run equilibrium price and agents supplied per agency as a function of the fixed cost, then figure out the fixed cost) M. Utku Ünver Micro Theory (BC) Firm and Industry Supply 26 / 26