© 2010 W. W. Norton & Company, Inc. 25 Monopoly Behavior

© 2010 W. W. Norton & Company, Inc. 2 How Should a Monopoly Price? u So 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. u Can price-discrimination earn a monopoly higher profits?

© 2010 W. W. Norton & Company, Inc. 3 Types of Price Discrimination u 1st-degree: Each output unit is sold at a different price. Prices may differ across buyers. u 2nd-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.

© 2010 W. W. Norton & Company, Inc. 4 Types of Price Discrimination u 3rd-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.

© 2010 W. W. Norton & Company, Inc. 5 First-degree Price Discrimination u Each output unit is sold at a different price. Price may differ across buyers. u It 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.

© 2010 W. W. Norton & Company, Inc. 6 First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $

© 2010 W. W. Norton & Company, Inc. 7 First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $ Later on sell the th unit for $

© 2010 W. W. Norton & Company, Inc. 8 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, $

© 2010 W. W. Norton & Company, Inc. 9 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.

© 2010 W. W. Norton & Company, Inc. 10 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

© 2010 W. W. Norton & Company, Inc. 11 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.

© 2010 W. W. Norton & Company, Inc. 12 First-degree Price Discrimination u First-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.

© 2010 W. W. Norton & Company, Inc. 13 Third-degree Price Discrimination u Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups.

© 2010 W. W. Norton & Company, Inc. 14 Third-degree Price Discrimination u A monopolist manipulates market price by altering the quantity of product supplied to that market. u So 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?”

© 2010 W. W. Norton & Company, Inc. 15 Third-degree Price Discrimination u Two markets, 1 and 2. u y 1 is the quantity supplied to market 1. Market 1’s inverse demand function is p 1 (y 1 ). u y 2 is the quantity supplied to market 2. Market 2’s inverse demand function is p 2 (y 2 ).

© 2010 W. W. Norton & Company, Inc. 16 Third-degree Price Discrimination u For given supply levels y 1 and y 2 the firm’s profit is u What values of y 1 and y 2 maximize profit?

© 2010 W. W. Norton & Company, Inc. 17 Third-degree Price Discrimination The profit-maximization conditions are

© 2010 W. W. Norton & Company, Inc. 18 Third-degree Price Discrimination The profit-maximization conditions are

© 2010 W. W. Norton & Company, Inc. 19 Third-degree Price Discrimination andso the profit-maximization conditions are and

© 2010 W. W. Norton & Company, Inc. 20 Third-degree Price Discrimination

© 2010 W. W. Norton & Company, Inc. 21 Third-degree Price Discrimination MR 1 (y 1 ) = MR 2 (y 2 ) says that the allocation y 1, y 2 maximizes the revenue from selling y 1 + y 2 output units. E.g., if MR 1 (y 1 ) > MR 2 (y 2 ) then an output unit should be moved from market 2 to market 1 to increase total revenue. 

© 2010 W. W. Norton & Company, Inc. 22 Third-degree Price Discrimination The marginal revenue common to both markets equals the marginal production cost if profit is to be maximized. 

© 2010 W. W. Norton & Company, Inc. 23 Third-degree Price Discrimination MR 1 (y 1 )MR 2 (y 2 ) y1y1 y2y2 y1*y1*y2*y2* p 1 (y 1 *) p 2 (y 2 *) MC p 1 (y 1 ) p 2 (y 2 ) Market 1Market 2 MR 1 (y 1 *) = MR 2 (y 2 *) = MC

© 2010 W. W. Norton & Company, Inc. 24 Third-degree Price Discrimination MR 1 (y 1 )MR 2 (y 2 ) y1y1 y2y2 y1*y1*y2*y2* p 1 (y 1 *) p 2 (y 2 *) MC p 1 (y 1 ) p 2 (y 2 ) Market 1Market 2 MR 1 (y 1 *) = MR 2 (y 2 *) = MC and p 1 (y 1 *)  p 2 (y 2 *).

© 2010 W. W. Norton & Company, Inc. 25 Third-degree Price Discrimination u In which market will the monopolist cause the higher price?

© 2010 W. W. Norton & Company, Inc. 26 Third-degree Price Discrimination u In which market will the monopolist cause the higher price? u Recall that and

© 2010 W. W. Norton & Company, Inc. 27 Third-degree Price Discrimination u In which market will the monopolist cause the higher price? u Recall that u But, and

© 2010 W. W. Norton & Company, Inc. 28 Third-degree Price Discrimination So

© 2010 W. W. Norton & Company, Inc. 29 Third-degree Price Discrimination So Therefore, if and only if

© 2010 W. W. Norton & Company, Inc. 30 Third-degree Price Discrimination So Therefore, if and only if

© 2010 W. W. Norton & Company, Inc. 31 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.

© 2010 W. W. Norton & Company, Inc. 32 Two-Part Tariffs u A two-part tariff is a lump-sum fee, p 1, plus a price p 2 for each unit of product purchased. u Thus the cost of buying x units of product is p 1 + p 2 x.

© 2010 W. W. Norton & Company, Inc. 33 Two-Part Tariffs u Should a monopolist prefer a two- part tariff to uniform pricing, or to any of the price-discrimination schemes discussed so far? u If so, how should the monopolist design its two-part tariff?

© 2010 W. W. Norton & Company, Inc. 34 Two-Part Tariffs u p 1 + p 2 x u Q: What is the largest that p 1 can be?

© 2010 W. W. Norton & Company, Inc. 35 Two-Part Tariffs u p 1 + p 2 x u Q: What is the largest that p 1 can be? u A: p 1 is the “market entrance fee” so the largest it can be is the surplus the buyer gains from entering the market. u Set p 1 = CS and now ask what should be p 2 ?

© 2010 W. W. Norton & Company, Inc. 36 Two-Part Tariffs p(y) y $/output unit MC(y) Should the monopolist set p 2 above MC?

© 2010 W. W. Norton & Company, Inc. 37 Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p 2 above MC? p 1 = CS. MC(y)

© 2010 W. W. Norton & Company, Inc. 38 Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p 2 above MC? p 1 = CS. PS is profit from sales. MC(y) PS

© 2010 W. W. Norton & Company, Inc. 39 Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p 2 above MC? p 1 = CS. PS is profit from sales. MC(y) PS Total profit

© 2010 W. W. Norton & Company, Inc. 40 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? MC(y)

© 2010 W. W. Norton & Company, Inc. 41 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. CS MC(y)

© 2010 W. W. Norton & Company, Inc. 42 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. PS is profit from sales. MC(y) CS PS

© 2010 W. W. Norton & Company, Inc. 43 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. PS is profit from sales. MC(y) CS Total profit PS

© 2010 W. W. Norton & Company, Inc. 44 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. PS is profit from sales. MC(y) CS PS

© 2010 W. W. Norton & Company, Inc. 45 Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. PS is profit from sales. MC(y) CS Additional profit from setting p 2 = MC. PS

© 2010 W. W. Norton & Company, Inc. 46 Two-Part Tariffs u The monopolist maximizes its profit when using a two-part tariff by setting its per unit price p 2 at marginal cost and setting its lump- sum fee p 1 equal to Consumers’ Surplus.

© 2010 W. W. Norton & Company, Inc. 47 Two-Part Tariffs u A profit-maximizing two-part tariff gives an efficient market outcome in which the monopolist obtains as profit the total of all gains-to-trade.

© 2010 W. W. Norton & Company, Inc. 48 Differentiating Products u In many markets the commodities traded are very close, but not perfect, substitutes. u E.g., the markets for T-shirts, watches, cars, and cookies. u Each individual supplier thus has some slight “monopoly power.” u What does an equilibrium look like for such a market?

© 2010 W. W. Norton & Company, Inc. 49 Differentiating Products u Free entry  zero profits for each seller.

© 2010 W. W. Norton & Company, Inc. 50 Differentiating Products u Free entry  zero profits for each seller. u Profit-maximization  MR = MC for each seller.

© 2010 W. W. Norton & Company, Inc. 51 Differentiating Products u Free entry  zero profits for each seller. u Profit-maximization  MR = MC for each seller. u Less than perfect substitution between commodities  slight downward slope for the demand curve for each commodity.

© 2010 W. W. Norton & Company, Inc. 52 Differentiating Products Price Quantity Supplied Demand Slight downward slope

© 2010 W. W. Norton & Company, Inc. 53 Differentiating Products Price Quantity Supplied Demand Marginal Revenue

© 2010 W. W. Norton & Company, Inc. 54 Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost

© 2010 W. W. Norton & Company, Inc. 55 Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost y* p(y*) Profit-maximization MR = MC

© 2010 W. W. Norton & Company, Inc. 56 Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost

© 2010 W. W. Norton & Company, Inc. 57 Differentiating Products u Such markets are monopolistically competitive. u Are these markets efficient? u No, because for each commodity the equilibrium price p(y*) > MC(y*).

© 2010 W. W. Norton & Company, Inc. 58 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*)

© 2010 W. W. Norton & Company, Inc. 59 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*) yeye

© 2010 W. W. Norton & Company, Inc. 60 Differentiating Products u Each seller supplies less than the efficient quantity of its product. u Also, each seller supplies less than the quantity that minimizes its average cost and so, in this sense, each supplier has “excess capacity.”

© 2010 W. W. Norton & Company, Inc. 61 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 yeye

© 2010 W. W. Norton & Company, Inc. 62 Differentiating Products by Location u Think a region in which consumers are uniformly located along a line. u Each consumer prefers to travel a shorter distance to a seller. u There are n ≥ 1 sellers. u Where would we expect these sellers to choose their locations?

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If n = 1 (monopoly) then the seller maximizes its profit at x = ?? 1 x

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If n = 1 (monopoly) then the seller maximizes its profit at x = ½ and minimizes the consumers’ travel cost. 1 x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If n = 2 (duopoly) then the equilibrium locations of the sellers, A and B, are x A = ?? and x B = ?? 1 x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If n = 2 (duopoly) then the equilibrium locations of the sellers, A and B, are x A = ?? and x B = ?? u How about x A = 0 and x B = 1; i.e. the sellers separate themselves as much as is possible? 1 x ½ AB

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If x A = 0 and x B = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. u Given B’s location at x B = 1, can A increase its profit? x ½ AB

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If x A = 0 and x B = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. u Given B’s location at x B = 1, can A increase its profit? What if A moves to x’? x ½ AB x’

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u If x A = 0 and x B = 1 then A sells to all consumers in [0,½) and B sells to all consumers in (½,1]. u Given B’s location at x B = 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 AB x’ x’/2

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u Given x A = x’, can B improve its profit by moving from x B = 1? x ½ AB x’

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u Given x A = x’, can B improve its profit by moving from x B = 1? What if B moves to x B = x’’? x ½ AB x’x’’

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u Given x A = x’, can B improve its profit by moving from x B = 1? What if B moves to x B = x’’? Then B sells to all customers in ((x’+x’’)/2,1] and increases its profit. u So what is the NE? x ½ AB x’x’’ (1-x’’)/2

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u Given x A = x’, can B improve its profit by moving from x B = 1? What if B moves to x B = x’’? Then B sells to all customers in ((x’+x’’)/2,1] and increases its profit. u So what is the NE? x A = x B = ½. x ½ A&B

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u The only NE is x A = x B = ½. u Is the NE efficient? x ½ A&B

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u The only NE is x A = x B = ½. u Is the NE efficient? No. u What is the efficient location of A and B? x ½ A&B

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u The only NE is x A = x B = ½. u Is the NE efficient? No. u What is the efficient location of A and B? x A = ¼ and x B = ¾ since this minimizes the consumers’ travel costs. x ½ A ¼¾ B

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u What if n = 3; sellers A, B and C? x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u What if n = 3; sellers A, B and C? u Then there is no NE at all! Why? x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u What if n = 3; sellers A, B and C? u Then there is no NE at all! Why? u 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. x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u (iii) Every seller locates at a different point. u Cannot be a NE since, as for n = 2, the two outside sellers get higher profits by moving closer to the middle seller. x ½

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u (i) All 3 sellers locate at the same point. u Cannot 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

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u (i) All 3 sellers locate at the same point. u Cannot 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 BAC C gets almost 1/2 of the market

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u 2 sellers locate at the same point. u Cannot be an NE since it pays one of the two sellers to move just a little away from the other. x ½ BAC A gets about 1/4 of the market

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u 2 sellers locate at the same point. u Cannot be an NE since it pays one of the two sellers to move just a little away from the other. x ½ C A gets almost 1/2 of the market B A

© 2010 W. W. Norton & Company, Inc Differentiating Products by Location u 2 sellers locate at the same point. u Cannot be an NE since it pays one of the two sellers to move just a little away from the other. x ½ C A gets almost 1/2 of the market B A

© 2010 W. W. Norton & Company, Inc. 86 Differentiating Products by Location u If 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. u There is no NE for n = 3.

© 2010 W. W. Norton & Company, Inc. 87 Differentiating Products by Location u If 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. u There is no NE for n = 3. u However, this is a NE for every n ≥ 4.