Hotelling s (1929) linear city. Hotelling

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1 US Manufacturing Industries C8 Average Profit ate >7 12.1% <7 6.9% Source: Bain, Joe S., "elation of Profit ate to Industry Concentration: American Manufacturing, ," Quarterly Journal of Economics, v. 6 (August 191), pp and Barriers to New Competition (Cambridge: Harvard University Press, 196). 1 Table 1: A Taxonomy of Market Structures Degree of Product Differentiation Firms produce identical Firms produce differentiated Number of firms (sellers) Many Few One Dominant Perfect Oligopoly with Competition homogeneous Monopolistic Competition Oligopoly with differentiated Dominant firm One Monopoly Market structures differ on four important dimensions: The number of sellers The number of buyers Entry conditions The degree of product differentiation Definition: Product Differentiation between two or more exists when the possess attributes that, in the minds of consumers, set the apart from one another and make them less than perfect substitutes. Examples: Pepsi is sweeter than Coke, Brand Name batteries last longer than "generic" batteries. 3 Two types of differentiation: "Superiority" (Vertical Product Differentiation) i.e. one product is viewed as unambiguously better than another so that, at the same price, all consumers would buy the better product "Substitutability" (Horizontal Product Differentiation) i.e. at the same price, some consumers would prefer the characteristics of product A while other consumers would prefer the characteristics of product B. 4 Hotelling s (1929) linear city Hotelling Why do all vendors locate in the same spot? For instance, on Cowick street they just opened a new Pharmacy right next to another one. Why do political parties (at least in the US) seem to have the same agenda? This can be explained by firms trying to get the most customers. L L Voters vote for the closest party. Party A Party B If Party A shifts to the right then it gains voters. Party A Party B Each has incentive to locate in the middle. 6 1

2 L L Hotelling Model Party A Party B Average distance for voter is ¼ total. This isn t efficient! Party A Party B Most efficient has average distance of 1/8 total. 7 Further considerations: Hotelling Firms choose location and then prices. Consumers care about both distance and price. If firms choose close together, they will eliminate profits as in Bertrand competition. If firms choose further apart, they will be able to make some profit. Thus, they choose further apart. 8 Example: Assume: Firms set price* Differentiated product Simultaneous Noncooperative As before, differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly Q 1 = - 2P 1 + P 2 "Coke's demand" Q 2 = - 2P 2 + P 1 "Pepsi's demand" MC 1 = MC 2 = What is firm 1's residual demand when Firm 2's price is $? $? Q 1 = - 2P 1 + = 1-2P 1 Q = - 2P 1 + = - 2P 1 9 Example: esidual Demand, Setting, Differentiated Products Example: esidual Demand, Setting, Differentiated Products Pepsi s price = $ for D and $ for D 1 Pepsi s price = $ for D and $ for D D D M

3 Example: esidual Demand, Setting, Differentiated Products 1 Pepsi s price = $ for D and $ for D Example: esidual Demand, Setting, Differentiated Products 1 Pepsi s price = $ for D and $ for D D D M D M D M 13 M 14 Example: esidual Demand, Setting, Differentiated Products 1 Pepsi s price = $ for D and $ for D Example: M 1 = - Q 1 = Q 1 = P 1 = 3 Therefore, firm 1's best response to a price of $ by firm 2 is a price of $3 3 D D M 4 M 1 16 Example: Solving for firm 1's reaction function for any arbitrary price by firm 2 P 1 = - Q 1 /2 + P 2 /2 M = - Q 1 + P 2 /2 And, using the demand curve, we have: P 1 = + P 2 /2-4/2 - P 2 /4 or P 1 = + P 2 /4 reaction function M = MC => Q 1 = 4 + P 2 /

4 Pepsi s price (P 2 ) Pepsi s price (P 2 ) P 1 = + P 2 /4 (Coke s.f.) P 2 = + P 1 /4 (Pepsi s.f.) P 2 = + P 1 /4 (Pepsi s.f.) Example: Equilibrium and eaction Functions, Setting and Differentiated Products Example: Equilibrium and eaction Functions, Setting and Differentiated Products (P 1 ) 19 P 1 = 1/3 (P 1 ) 2 P 2 = 1/3 Pepsi s price (P 2 ) Bertrand Equilibrium P 1 = + P 2 /4 (Coke s.f.) P 2 = + P 1 /4 (Pepsi s.f.) Example: Equilibrium and eaction Functions, Setting and Differentiated Products Equilibrium: Equilibrium occurs when all firms simultaneously choose their best response to each others' actions. Graphically, this amounts to the point where the best response functions cross... P 1 = 1/3 (P 1 ) Example: Firm 1 and firm 2, continued P 1 = + P 2 /4 P 2 = + P 1 /4 Solving these two equations in two unknowns P 1* = P 2* = 1/3 Plugging these prices into demand, we have: Q 1* = Q 2* = 19/3 π 1* = π 2* = 2. Π = 411. Notice that 1. profits are positive in equilibrium since both prices are above marginal cost! Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price This blunts price-cutting incentives and means that the firms' own behavior does not mimic free entry

5 Only if I were to let the number of firms approach infinity would price approach marginal cost. 2. s need not be equal in equilibrium if firms not identical (e.g. Marginal costs differ implies that prices differ) 3. The reaction functions slope upward: "aggression => aggression" 2 7. Equilibrium in such a setting requires that all firms be on their best response functions. 8. If the are homogeneous, the Bertrand equilibrium results in zero profits. By changing the strategic variable from price to quantity, we obtain much higher prices (and profits). Further, the results are sensitive to the assumption of simultaneous moves. 9. This result can be traced to the slope of the reaction functions: upwards in the case of Bertrand and downwards in the case of Cournot. These slopes imply that "aggressivity" results in a "passive" response in the Cournot case and an "aggressive" response in the Bertrand case. 26 (Chamberlinian) Monopolistic Competition Market Structure: Many Buyers Many Sellers Free entry and Exit (Horizontal) Product Differentiation Monopolistic Competition in the Short un: (fixed number of firms) 1. Each firm is small => each takes the observed "market price" as given in its production decisions. 2. Since market price may not stay given, the firm's perceived demand may differ from its actual demand. When firms have horizontally differentiated, they each face downward-sloping demand for their product because a small change in price will not cause ALL buyers to switch to another firm's product If all firms' prices fall the same amount, no customers switch supplier but the total market consumption grows. 4. If only one firm's price falls, it steals customers from other firms as well as increases total market consumption 28 Example: Perceived Demand and Actual Demand Example: Perceived Demand and Actual Demand d (P A =) d (P A =2) d (P A =2) 29 3

6 Example: Perceived Demand and Actual Demand The market is in equilibrium if each firm maximizes profit taking the average market price as given Demand (assuming price by all firms) d (P A =) d (P A =2) 31 each firm can sell the quantity it desires at the actual average market price that prevails 32 Example: Short un Chamberlinian Equilibrium Example: Short un Chamberlinian Equilibrium d (P A =) Example: Short un Chamberlinian Equilibrium Example: Short un Chamberlinian Equilibrium Demand (assuming price by all firms P=P A ) Demand (assuming price by all firms P=P A ) 43 d (P A =) 1 mc d (P A =) 3 7 M

7 Example: Computing A Short-un Monopolistically Competitive Equilibrium MC = $1 N = Q = - 2P + P A Where: P A is the average market price N is the number of firms a. What is the equation of d 4? What is the equation of D? d 4 : Q d = - 2P + 4 = 14-2P D: Note that P = P A so that Q D = - P b. Show that d 4 and D intersect at P = 4 P = 4 => Q d = 14-8 = 6 Q D = - 4 = 6 c. For any given average price, P A, find a typical firm's profit maximizing quantity Inverse (perceived) demand: P = - (1/2)Q + (1/2)P A M = - Q + (1/2)P A M = MC => - Q + (1/2)P A = 1 d. What is the short run equilibrium price in this industry? In equilibrium, Q e = Q D at P A so that - P A = 3 + (1/2)P A P A = Q e = 6.66 Q D = 6.66 Q e = 3 + (1/2)P A P e = - (1/2)Q e + (1/2)P A P e = (1/4)P A 39 4 Monopolistic Competition in the Long un At the short run equilibrium P > AC so that each firm may make positive profit. Example: Long un Chamberlinian Equilibrium esidual Demand shifts in as entry occurs Entry shifts d and D left until average industry price equals average cost. This is long run equilibrium is represented graphically by: P* P** Marginal Cost M = MC for each firm D = d at the average market price d and AC are tangent at average market price 41 q** q* M Average Cost 42 7