# Firm Supply. Market demand. Demand curve facing firm

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1 Firm Supply 84 Firm Supply A. Firms face two sorts of constraints 1. technological constraints summarize in cost function 2. market constraints how will consumers and other firms react to a given firm s choice? B. Pure competition 1. formally takes market price as given, outside of any particular firm s control 2. example: many small price takers 3. demand curve facing a competitive firm Figure p Market demand Market price p* Demand curve facing firm y Figure 21.1 C. Supply decision of competitive firm 1. max y py c(y) 2. first-order condition: p = c (y) 3. price equals marginal cost determines supply as function of price 4. second-order condition: c (y) 0, or c (y) only upward-sloping part of marginal cost curve matters 6. is it profitable to operate at all? a) compare py c v (y) F with F b) profits from operating will be greater when p>c v (y)/y c) operate when price covers average variable costs

2 Firm Supply 85 D. So supply curve is the upward-sloping part of curve that lies above the AV C curve 1. see Figure AVC AVC y Figure 21.3 E. Inverse supply curve 1. p = c (y) measures the marginal cost curve directly F. Example: c(y) =y p =2y gives the (inverse) supply curve 2. is p AV C? a) yes, since 2y y for all y 0 3. see Figure G. Producer s surplus 1. producer s surplus is defined to be py c v (y) 2. since c v (y) = area under marginal cost curve 3. producer s surplus is also the area above the marginal cost curve 4. we can also use the rectangle for part of PS and the area above fortherest 5. see Figure H. Long-run supply use long-run. In long run, price must be greater than

3 Firm Supply 86 p = supply curve AVC 2 Producer's surplus 1 y Figure 21.7 AVC p = S AVC p = S AVC AVC z y OUTPUT A Revenue variable costs z y OUTPUT B Area above curve AVC p R T = S AVC z y OUTPUT C Area to the left of the supply curve Figure 21.5 I. Special case constant average cost (CRS): flat supply curve 1. see Figure

4 Firm Supply 87 p C min L = long-run supply y Figure 21.10

5 Industry Supply 88 Industry Supply A. Short-run industry supply 1. sum of the curves 2. equilibrium in short run a) look for point where D(p) =S(p) b) can then measure profits of firms c) see Figure p p p p* y y y Firm A Firm B Firm C Figure 22.2 B. Long-run industry supply 1. change to long-run technology 2. entry and exit by firms a) look at curves with different number of firms b) find lowest curve consistent with nonnegative profits c) see Figure C. Long-run supply curve 1. exact see Figure approximate flat at p = minimum 3. like replication argument

6 Industry Supply 89 p S 1 S 2 S 3 A S 4 p' p* D'' D y Figure 22.3 p S1 S2 S3 S4 p* y Figure 22.4 D. Taxation in long and short runs

7 Industry Supply 90 PRICE Shifted short-run supply P" D P' D P" S = P S = PD Demand Short-run supply Tax Shifted long-run supply Long-run supply P' S QUANTITY Figure see Figure in industry with entry and exit 3. part of tax is borne by each side 4. long run all borne by consumers E. Meaning of zero profits 1. pure economic profit means anyone can get it 2. a mature industry may show accounting profits, but economic profits are probably zero F. Economic rent 1. what if some factors are scarce in the long run? a) licenses liquor, taxicab b) raw materials, land, etc. 2. fixed from viewpoint of industry, variable from viewpoint of firm 3. in this case, industry can only support a certain number of firms 4. whatever factor is preventing entry earns rents a) always the possibility of entry that drives profits to zero b) if profits are being made, firms enter industry by 1) bringing in new resources 2) bidding up prices of existing resources

8 Industry Supply 91 AVC (including rent) = supply curve p* AVC (excluding rent) Rent y* y Figure see Figure discount flow of rents to get asset value 7. politics of rent a) rents are a pure surplus payment b) but people compete for those rents c) taxicab licenses current holders want very much to prevent entry d) subsidies and rents incidence of subsidy falls on the rents 1) tobacco subsidies 2) farm policy in general e) rent seeking G. Energy policy 1. two-tiered oil pricing 2. price controls 3. entitlement program

9 Monopoly 92 Monopoly A. Profit maximization 1. max r(y) c(y) implies r (y) =c (y) 2. max p(y)y c(y) implies p(y)+p (y)y = c (y) 3. can also write this as p(y) [ 1+ dp dy ] y = c (y) p 4. or p(y)[1 + 1/ɛ] =c (y) 5. linear case a) in case of linear demand, p = a by, marginal revenue is given by MR = a 2by b) see Figure PRICE a Profits = π p* MR (slope = 2b) Demand (slope = b) y* OUTPUT 6. constant elasticity, q = Ap ɛ a) in this case, MR = p[1 + 1/ɛ] b) so, optimal condition is p[1 + 1/ɛ] =c (y) c) markup on marginal cost d) see Figure Figure 23.1 B. Taxes 1. linear case price goes up by half of tax. Figure log case price goes up by more than tax, since price is a markup on

10 Monopoly 93 PRICE 1 1/ ε p* Demand y* OUTPUT Figure 23.2 PRICE Δp { p' p* After tax Before tax { t + t MR Demand y' y* OUTPUT Figure 23.3 C. Inefficiency of monopoly

11 Monopoly Pareto efficient means no way to make some group better off without hurting some other group 2. Pareto inefficient means that there is some way to make some group better off without hurting some other group 3. monopoly is Pareto inefficient since P> 4. measure of the deadweight loss value of lost output 5. see Figure PRICE p* = monopoly price Competitive price A B C Demand MR y* OUTPUT Figure 23.5 D. Patents 1. sometimes we want to pay this cost of inefficiency 2. patents: trade-off of innovation against monopoly losses E. Natural monopoly 1. public utilities (gas, electricity, telephone) are often thought of as natural monopolies 2. occurs when p = mc is unprofitable decreasing 3. Figure often occurs when fixed costs are big and marginal costs are small 5. how to handle a) government operates and covers deficit from general revenues b) regulates pricing behavior so that price =

12 Monopoly 95 PRICE Demand p p Losses to the firm from marginal cost pricing y y OUTPUT Figure 23.6 F. Cause of monopoly 1. MES large relative to size of market 2. collusion 3. law (oranges, sports, etc.) 4. trademarks, copyrights, brand names, etc.

13 Monopoly Behavior 96 Monopoly Behavior A. Price discrimination 1. first degree perfect price discrimination a) gives Pareto efficient output b) same as take-it-or-leave-it offer c) producer gets all surplus 2. second degree nonlinear pricing a) two demand curves b) would like to charge each full surplus c) but have to charge bigger one less to ensure self-selection d) but then want to reduce the amount offered to smaller consumer 3. third degree most common a) max p 1 (y 1 )y 1 + p 2 (y 2 )y 2 c(y 1 + y 2 ) b) gives us the first-order conditions p 1 + p 1 (y 1)y 1 = c (y 1 + y 2 ) p 2 + p 2(y 2 )y 2 = c (y 1 + y 2 ) c) or [ p ] = ɛ 1 [ p ] = ɛ 2 d) result: if p 1 >p 2,then ɛ 1 < ɛ 2 e) more elastic users pay lower prices B. Two-part tariffs 1. what happens if everyone is the same? 2. entrance fee = full surplus 3. usage fee = marginal cost C. Bundling 1. type A: wtp \$120 for word processor, \$100 for spreadsheet 2. type B: wtp \$100 for word processor, \$120 for spreadsheet 3. no bundling profits = \$ bundling profits =\$ reduce dispersion of wtp

14 Monopoly Behavior 97 PRICE p* Demand y* y Figure 24.3 D. Monopolistic competition 1. rare to see pure monopoly 2. product differentiation so some market power 3. free entry 4. result excess capacity theorem a) see Figure b) (but is it really?) 5. location model of product differentiation a) ice cream vendors on the boardwalk b) socially optimal to locate at 1/4 and3/4 c) but this is unstable d) only stable configuration is for both to locate at middle e) is there too much conformity in differentiated markets?

15 Factor Markets 98 Factor Markets A. Monopoly in output market 1. marginal product, MP x 2. marginal revenue, MR y 3. marginal revenue product, MRP x 4. value of the marginal [ ] product, pmp x a) MRP = p 1 1 ɛ b) note that this is less than value of MP B. Monopoly/monoposony in input market 1. market power by demander of factor 2. maximize pf(x) w(x)x 3. get MR =, but with particular form 4. now = w [ ] 1+ 1 ɛ 5. linear example: Figure w MR = = a + 2bL w (L) = a + bl (inverse supply) w * a MR = pmpl L* LABOR Figure minimum wage

16 Factor Markets 99 C. Upstream and downstream monopoly 1. one monopolist produces a factor that he sells to another monopolist 2. suppose that one unit of the input produces one unit of output in downstream monopolist 3. each monopolist wants to mark up its output price over marginal cost 4. results in a double markup 5. if firms integrated, would only have a single markup 6. price would go down

17 Oligopoly 100 Oligopoly A. Oligopoly is the study of the interaction of a small number of firms 1. duopoly is simplest case 2. unlikely to have a general solution; depends on market structure and specific details of how firms interact B. Classification of theories 1. non-collusive a) sequential moves 1) quantity setting Stackelberg 2) price setting price leader b) simultaneous moves 1) quantity setting Cournot 2) price setting Bertrand 2. collusive C. Stackelberg behavior 1. asymmetry one firm, quantity leader, gets to set quantity first 2. maximize profits, given the reaction behavior of the other firm 3. take into response that the other firm will follow my lead 4. analyze in reverse 5. firm 2 a) max y2 P (y 1 + y 2 )y 2 c(y 2 ) b) FOC: P (y 1 + y 2 )+P (y 1 + y 2 )y 2 = c (y 2 ) c) solution gives reaction function, f 2 (y 1 ) 6. firm 1 a) max y1 P (y 1 + f 2 (y 1 ))y 1 c(y 1 ) b) FOC: P (y 1 + f 2 (y 1 )) + P (y 1 + f 2 (y 1 ))y 1 = c (y 1 ) c) see Figure graphical solution in Figure D. Price-setting behavior 1. leader sets price, follower takes it as given 2. given p 1, firm 2 supplies S 2 (p 1 ) 3. if demand is D(p), this leaves D(p 1 ) S 2 (p 1 ) for leader 4. hence leader wants to maximize p 1 y 1 c(y 1 ) such that y 1 = D(p 1 ) S 2 (p 1 ) 5. leader faces residual demand curve

18 Oligopoly 101 y 2 Reaction curve for firm 1 Reaction curve for firm 2 Cournot equilibrium Stackelberg equilibrium Isoprofit curves for firm1 y 1 Figure 26.2 y 2 = OUTPUT OF FIRM 2 Reaction curve f (y ) 1 2 y* 2 (y t + 4 1, y t ) (y t + 2 1, y t ) (y t + 3 1, y t ) (y t + 1 t + 1, y 1 2 ) Possible adjustment to equilibrium Reaction curve f 2(y 1) t t (y 1, y 2) y* 1 y 1 = OUTPUT OF FIRM 1 Figure 26.4 E. Cournot equilibrium simultaneous quantity setting 1. each firm makes a choice of output, given its forecast of the other firm s output

19 Oligopoly let y 1 be the output choice of firm 1 and y e 2 be firm 1 s beliefs about firm 2 s output choice 3. maximization problem max y1 p(y 1 + y e 2)y 1 c(y 1 ) 4. let Y = y 1 + y e 2 5. first-order condition is p(y )+p (Y )y 1 = c (y 1 ) 6. this gives firm 1 s reaction curve how it chooses output given its beliefs about firm 2 s output 7. see Figure y 2 = OUTPUT OF FIRM 2 Isoprofit lines for firm 2 f 2 (y 1 ) Reaction curve f 2(y 1) y 1 y 1 = OUTPUT OF FIRM 1 Figure look for Cournot equilibrium where each firm finds its expectations confirmed in equilibrium 9. so y 1 = y1 e and y 2 = y2 e F. Example of Cournot 1. assume zero costs 2. linear demand function p(y )=a by 3. profit function: [a b(y 1 + y 2 )]y 1 = ay 1 by1 2 by 1 y 2 4. derive reaction curve a) maximize profits b) a 2by 1 by 2 =0 c) calculate to get y 1 =(a by 2 )/2b d) do same sort of thing to get reaction curve for other firm 5. look for intersection of reaction curves

20 Oligopoly 103 G. Bertrand simultaneous price setting 1. consider case with constant identical marginal cost 2. if firm 1 thinks that other firm will set p 2, what should it set? 3. if I think p 2 is greater than my,setp 1 slightly smaller than p 2 4. I get all the customers and make positive profits 5. only consistent (equilibrium) beliefs are p 1 = p 2 = H. Collusion 1. firms get together to maximize joint profits 2. marginal impact on joint profits from selling output of either firm must be the same 3. max p(y 1 + y 2 )[y 1 + y 2 ] c(y 1 ) c(y 2 ) 4. P (y 1 + y 2 )+P (y 1 + y 2 )[y 1 + y 2 ]=c (y 1 )=c (y 2 ) 5. note instability if firm 1 believes firm 2 will keep its output fixed, it will always pay it to increase its own output 6. problems with OPEC 7. if it doesn t believe other firm will keep its output fixed, it will cheat first!

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