microlower.jpg © 2010 W. W. Norton & Company, Inc. microtitle.jpg microedition.jpg varianname.jpg 25 Monopoly Behavior microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› How Should a Monopoly Price? uSo far a monopoly has been thought of as a firm which has to sell its product at the same price to every customer. This is uniform pricing. uCan price-discrimination earn a monopoly higher profits? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Types of Price Discrimination u1st-degree: Each output unit is sold at a different price. Prices may differ across buyers. u2nd-degree: The price paid by a buyer can vary with the quantity demanded by the buyer. But all customers face the same price schedule. E.g., bulk-buying discounts. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Types of Price Discrimination u3rd-degree: Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. E.g., senior citizen and student discounts vs. no discounts for middle-aged persons. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination uEach output unit is sold at a different price. Price may differ across buyers. uIt requires that the monopolist can discover the buyer with the highest valuation of its product, the buyer with the next highest valuation, and so on. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $ Later on sell the th unit for $ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $ Later on sell the th unit for $ Finally sell the th unit for marginal cost, $ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) The gains to the monopolist on these trades are: and zero. The consumers’ gains are zero. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) So the sum of the gains to the monopolist on all trades is the maximum possible total gains-to-trade. PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination p(y) y $/output unit MC(y) The monopolist gets the maximum possible gains from trade. PS First-degree price discrimination is Pareto-efficient. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› First-degree Price Discrimination uFirst-degree price discrimination gives a monopolist all of the possible gains-to-trade, leaves the buyers with zero surplus, and supplies the efficient amount of output. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uPrice paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uA monopolist manipulates market price by altering the quantity of product supplied to that market. uSo the question “What discriminatory prices will the monopolist set, one for each group?” is really the question “How many units of product will the monopolist supply to each group?” microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uTwo markets, 1 and 2. uy1 is the quantity supplied to market 1. Market 1’s inverse demand function is p1(y1). uy2 is the quantity supplied to market 2. Market 2’s inverse demand function is p2(y2). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uFor given supply levels y1 and y2 the firm’s profit is uWhat values of y1 and y2 maximize profit? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination The profit-maximization conditions are microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination The profit-maximization conditions are microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination and so the profit-maximization conditions are and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination MR1(y1) = MR2(y2) says that the allocation y1, y2 maximizes the revenue from selling y1 + y2 output units. E.g., if MR1(y1) > MR2(y2) then an output unit should be moved from market 2 to market 1 to increase total revenue. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination The marginal revenue common to both markets equals the marginal production cost if profit is to be maximized. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination MR1(y1) MR2(y2) y1 y2 y1* y2* p1(y1*) p2(y2*) MC MC p1(y1) p2(y2) Market 1 Market 2 MR1(y1*) = MR2(y2*) = MC microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination MR1(y1) MR2(y2) y1 y2 y1* y2* p1(y1*) p2(y2*) MC MC p1(y1) p2(y2) Market 1 Market 2 MR1(y1*) = MR2(y2*) = MC and p1(y1*) ¹ p2(y2*). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uIn which market will the monopolist cause the higher price? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uIn which market will the monopolist cause the higher price? uRecall that and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination uIn which market will the monopolist cause the higher price? uRecall that uBut, and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination So microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination So Therefore, if and only if microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination So Therefore, if and only if microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Third-degree Price Discrimination So Therefore, if and only if The monopolist sets the higher price in the market where demand is least own-price elastic. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs uA two-part tariff is a lump-sum fee, p1, plus a price p2 for each unit of product purchased. uThus the cost of buying x units of product is p1 + p2x. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs uShould a monopolist prefer a two-part tariff to uniform pricing, or to any of the price-discrimination schemes discussed so far? uIf so, how should the monopolist design its two-part tariff? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs u p1 + p2x uQ: What is the largest that p1 can be? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs u p1 + p2x uQ: What is the largest that p1 can be? uA: p1 is the “market entrance fee” so the largest it can be is the surplus the buyer gains from entering the market. uSet p1 = CS and now ask what should be p2? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit MC(y) Should the monopolist set p2 above MC? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p2 above MC? p1 = CS. MC(y) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p2 above MC? p1 = CS. PS is profit from sales. MC(y) PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p2 above MC? p1 = CS. PS is profit from sales. MC(y) PS Total profit microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? MC(y) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? p1 = CS. CS MC(y) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? p1 = CS. PS is profit from sales. MC(y) CS PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? p1 = CS. PS is profit from sales. MC(y) CS Total profit PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? p1 = CS. PS is profit from sales. MC(y) CS PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs p(y) y $/output unit Should the monopolist set p2 = MC? p1 = CS. PS is profit from sales. MC(y) CS Additional profit from setting p2 = MC. PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs uThe monopolist maximizes its profit when using a two-part tariff by setting its per unit price p2 at marginal cost and setting its lump-sum fee p1 equal to Consumers’ Surplus. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Two-Part Tariffs uA profit-maximizing two-part tariff gives an efficient market outcome in which the monopolist obtains as profit the total of all gains-to-trade. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uIn many markets the commodities traded are very close, but not perfect, substitutes. uE.g., the markets for T-shirts, watches, cars, and cookies. uEach individual supplier thus has some slight “monopoly power.” uWhat does an equilibrium look like for such a market? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uFree entry Þ zero profits for each seller. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uFree entry Þ zero profits for each seller. uProfit-maximization Þ MR = MC for each seller. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uFree entry Þ zero profits for each seller. uProfit-maximization Þ MR = MC for each seller. uLess than perfect substitution between commodities Þ slight downward slope for the demand curve for each commodity. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Slight downward slope microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost y* p(y*) Profit-maximization MR = MC microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uSuch markets are monopolistically competitive. uAre these markets efficient? uNo, because for each commodity the equilibrium price p(y*) > MC(y*). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost MC(y*) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost MC(y*) ye microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products uEach seller supplies less than the efficient quantity of its product. uAlso, each seller supplies less than the quantity that minimizes its average cost and so, in this sense, each supplier has “excess capacity.” microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost MC(y*) Excess capacity ye microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products by Location uThink a region in which consumers are uniformly located along a line. uEach consumer prefers to travel a shorter distance to a seller. uThere are n ≥ 1 sellers. uWhere would we expect these sellers to choose their locations? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 0 Differentiating Products by Location uIf n = 1 (monopoly) then the seller maximizes its profit at x = ?? 1 x microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 0 Differentiating Products by Location uIf n = 1 (monopoly) then the seller maximizes its profit at x = ½ and minimizes the consumers’ travel cost. 1 x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 0 Differentiating Products by Location uIf n = 2 (duopoly) then the equilibrium locations of the sellers, A and B, are xA = ?? and xB = ?? 1 x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 0 Differentiating Products by Location uIf n = 2 (duopoly) then the equilibrium locations of the sellers, A and B, are xA = ?? and xB = ?? uHow about xA = 0 and xB = 1; i.e. the sellers separate themselves as much as is possible? 1 x ½ A B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uIf xA = 0 and xB = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. uGiven B’s location at xB = 1, can A increase its profit? x ½ A B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uIf xA = 0 and xB = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. uGiven B’s location at xB = 1, can A increase its profit? What if A moves to x’? x ½ A B x’ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uIf xA = 0 and xB = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. uGiven B’s location at xB = 1, can A increase its profit? What if A moves to x’? Then A sells to all customers in [0,½+½ x’) and increases its profit. x ½ A B x’ x’/2 microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uGiven xA = x’, can B improve its profit by moving from xB = 1? x ½ A B x’ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uGiven xA = x’, can B improve its profit by moving from xB = 1? What if B moves to xB = x’’? x ½ A B x’ x’’ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uGiven xA = x’, can B improve its profit by moving from xB = 1? What if B moves to xB = x’’? Then B sells to all customers in ((x’+x’’)/2,1] and increases its profit. uSo what is the NE? x ½ A B x’ x’’ (1-x’’)/2 microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uGiven xA = x’, can B improve its profit by moving from xB = 1? What if B moves to xB = x’’? Then B sells to all customers in ((x’+x’’)/2,1] and increases its profit. uSo what is the NE? xA = xB = ½. x ½ A&B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uThe only NE is xA = xB = ½. uIs the NE efficient? x ½ A&B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uThe only NE is xA = xB = ½. uIs the NE efficient? No. uWhat is the efficient location of A and B? x ½ A&B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uThe only NE is xA = xB = ½. uIs the NE efficient? No. uWhat is the efficient location of A and B? xA = ¼ and xB = ¾ since this minimizes the consumers’ travel costs. x ½ A ¼ ¾ B microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uWhat if n = 3; sellers A, B and C? x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uWhat if n = 3; sellers A, B and C? uThen there is no NE at all! Why? x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location uWhat if n = 3; sellers A, B and C? uThen there is no NE at all! Why? uThe possibilities are: –(i) All 3 sellers locate at the same point. –(ii) 2 sellers locate at the same point. –(iii) Every seller locates at a different point. x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u(iii) Every seller locates at a different point. uCannot be a NE since, as for n = 2, the two outside sellers get higher profits by moving closer to the middle seller. x ½ microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u(i) All 3 sellers locate at the same point. uCannot be an NE since it pays one of the sellers to move just a little bit left or right of the other two to get all of the market on that side, instead of having to share those customers. x ½ A B C C gets 1/3 of the market microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u(i) All 3 sellers locate at the same point. uCannot be an NE since it pays one of the sellers to move just a little bit left or right of the other two to get all of the market on that side, instead of having to share those customers. x ½ B A C C gets almost 1/2 of the market microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u2 sellers locate at the same point. uCannot be an NE since it pays one of the two sellers to move just a little away from the other. u x ½ B A C A gets about 1/4 of the market microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u2 sellers locate at the same point. uCannot be an NE since it pays one of the two sellers to move just a little away from the other. u x ½ C A gets almost 1/2 of the market B A microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› 1 0 Differentiating Products by Location u2 sellers locate at the same point. uCannot be an NE since it pays one of the two sellers to move just a little away from the other. u x ½ C A gets almost 1/2 of the market B A microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products by Location uIf n = 3 the possibilities are: –(i) All 3 sellers locate at the same point. –(ii) 2 sellers locate at the same point. –(iii) Every seller locates at a different point. uThere is no NE for n = 3. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Differentiating Products by Location uIf n = 3 the possibilities are: –(i) All 3 sellers locate at the same point. –(ii) 2 sellers locate at the same point. –(iii) Every seller locates at a different point. uThere is no NE for n = 3. uHowever, this is a NE for every n ≥ 4.