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Chapter Twenty-Five Monopoly Behavior

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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?

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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.

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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.

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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.

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First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $

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First-degree Price Discrimination p(y) y $/output unit MC(y) Sell the th unit for $ Later on sell the th unit for $

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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, $

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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.

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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

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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.

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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.

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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.

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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?

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Third-degree Price Discrimination u Two markets, 1 and 2. u y 1 is the quantity supplied to market 1. Market 1s inverse demand function is p 1 (y 1 ). u y 2 is the quantity supplied to market 2. Market 2s inverse demand function is p 2 (y 2 ).

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Third-degree Price Discrimination u For given supply levels y 1 and y 2 the firms profit is u What values of y 1 and y 2 maximize profit?

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Third-degree Price Discrimination The profit-maximization conditions are

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Third-degree Price Discrimination The profit-maximization conditions are

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Third-degree Price Discrimination andso the profit-maximization conditions are and

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Third-degree Price Discrimination

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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.

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Third-degree Price Discrimination The marginal revenue common to both markets equals the marginal production cost if profit is to be maximized.

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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

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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 *).

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Third-degree Price Discrimination u In which market will the monopolist cause the higher price?

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Third-degree Price Discrimination u In which market will the monopolist cause the higher price? u Recall that and

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Third-degree Price Discrimination u In which market will the monopolist cause the higher price? u Recall that u But, and

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Third-degree Price Discrimination So

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Third-degree Price Discrimination So Therefore, if and only if

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Third-degree Price Discrimination So Therefore, if and only if

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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.

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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.

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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?

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Two-Part Tariffs u p 1 + p 2 x u Q: What is the largest that p 1 can be?

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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 ?

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Two-Part Tariffs p(y) y $/output unit MC(y) Should the monopolist set p 2 above MC?

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Two-Part Tariffs p(y) y $/output unit CS Should the monopolist set p 2 above MC? p 1 = CS. MC(y)

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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

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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

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Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? MC(y)

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Two-Part Tariffs p(y) y $/output unit Should the monopolist set p 2 = MC? p 1 = CS. CS MC(y)

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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

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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

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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

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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

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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.

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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.

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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?

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Differentiating Products u Free entry zero profits for each seller.

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Differentiating Products u Free entry zero profits for each seller. u Profit-maximization MR = MC for each seller.

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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.

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Differentiating Products Price Quantity Supplied Demand Slight downward slope

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Differentiating Products Price Quantity Supplied Demand Marginal Revenue

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Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost

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Differentiating Products Price Quantity Supplied Demand Marginal Revenue Marginal Cost y* p(y*) Profit-maximization MR = MC

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Differentiating Products Price Quantity Supplied Demand Marginal Revenue Average Cost Marginal Cost y* p(y*) Profit-maximization MR = MC Zero profit Price = Av. Cost

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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*).

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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*)

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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

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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.

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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

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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?

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0 Differentiating Products by Location 1 x u If n = 1 (monopoly) then the seller maximizes its profit at x = ??

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0 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

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0 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

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0 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

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10 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 Bs location at x B = 1, can A increase its profit? x ½ AB

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10 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 Bs location at x B = 1, can A increase its profit? What if A moves to x? x ½ AB x

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10 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 Bs 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

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10 Differentiating Products by Location u Given x A = x, can B improve its profit by moving from x B = 1? x ½ AB x

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10 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 xx

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10 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 xx (1-x)/2

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10 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

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10 Differentiating Products by Location u The only NE is x A = x B = ½. u Is the NE efficient? x ½ A&B

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10 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

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10 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

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10 Differentiating Products by Location u What if n = 3; sellers A, B and C? x ½

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10 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

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10 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

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10 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

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10 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

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10 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

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10 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

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10 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

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10 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

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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.

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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.

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