Price Discrimination

Transcription

1 Price Discrimination Firm charges either di erent consumers, di erent prices for the same product supplied with identical costs or di erent consumers the same price even though the cost of supplying them may vary to di erent consumers Example: Student tickets, Auction?, airline tickets, golf club membership, coupons. First degree price dicrimination: each consumer pays teh highest he or she is willing to pay. Before 00, Microsoft used a form rst degree price dicrimination to give license for its operating system to the computer manufacurers such as Dell, Gateway, HP and IBM. Consider P = 0 Q and production costs of MC = AC = : The standard monopolist would sell 4 units at 6 per unit. The perfectly discriminating monopolist charges the price: the rst unit is sold at 9, the second at 8, the third at 7, till the eith is sold at. Total revenue is The standar monopolist gets a producer surplus of Y, but the perfectly discriminating monopolist is able to extract X from the consumer as well as get Z. Third degree price dicrimination: rms charge di erent prices for the same good to di erent groups. Example: Student lm tickets or bus tickets for pensioners. rms are able to seperate the groups according to their demand elasticities. consumers cannot self-select into di erent groups, i.e., consumers can be identi ed according to the groups they belong to and therefore they cannot cheat. Let the local Odeon recognize it faces two distict demand curves, one for senior citizens above 65 yrs, p s = 5 30 q s; and the other for adults below 65 yrs age, p a = 0 0 q a. Let MC = AC = To maximize pro ts, Odeon equates marginal revenue in each market, 65+ and below 65, to its marginal cost.

2 So in the 65 and below market, marginal revenue, MR a is 0 5 q a: 0 5 q a = q a = 45 p a = 0 0 q a = 5:5 In the 65 and below market, marginal revenue, MR s is 5 5 q s: 5 5 q s = q s = 60 p s = 5 30 q s = 3 Demand Elasticity for the adults below age of 65 p q 5:5 = 0 45 = Demand Elasticity for the adults above age of p q = 30 3 :5 60 = If only one price was charged: then the price would be p = 3:65, and q = 05 Social welfare is higher if single price is charged. Second degree price discrimination: All consumers are given the same price schedule and then the consumers self select. quantity discount used when the the seller or rm cannot distinguish between the consumers with di erent reservation price. Examples: Pizza Hut, Airline prices. Consider Levi s produces a pair of jeans for MC = AC = 0: And o ers a quantity discount: buy one pair for 80, second pair for 60, third pairs for 40 and the fourth pair for 0. Consider that Levi s sells jeans to 0 consumers in each of the four categories each day. So 40 buyers buy the rst pair at 80, 30 buyers purchase the second pair at 60, 0 buyers purchase the second pair at 40, 0 buyers purchase the second pair at 0. So the total quantity is 00 and the total revenue is =6000 Two part tari : Disney world pricing: Entrance fee and price per ride. Rent charge for copier and then price per copy made.

3 Clubs: Entry fee and price per beer. Consider copying machine market where the seller cannot distinguish between the buyers but knows there are two type of consumers A and B, and the they are equal in number. Type A has the demand function p = 00 q A Type A has the demand function p = 00 q B Assume monthly xed costs are 500 for the seller and the marginal costs per copy is zero. Assume for simplicity that there is one of each type of consumer. So the maximum Type A buyers would be willing to pay is (00) (00) = 5000, and maximum Type B buyers would be willing to pay is (00) (50) = 500 If the seller uses a single price strategy then the seller will either charge 5000 and sell only to type A or charge 500 and sell to both. If it charges 5000 then the pro t is = 4500, and if it charges 500 then the pro t is ( ) = 4000: Consider now the two part tari : the seller decides to sell to both kinds of buyers and charge a rental fee for the machine and a price per copy. Pro t = (fixed fee) + p(q A + q B ) (fixed cos ts) The xed fee rental has to be set in order to extract the maximum consumer surplus possible. We will claim that this xed fee has to be equal to the whole consumer surplus of the inelatic type buyer, i.e., buyer of type B. So if the copies are priced at price p: The consumer surplus of type B is CS B = (00 p) q = (00 p) 50 So at p, the total demand has to be q A + q B From p = 00 q A ; q A = 00 p From p = 00 q B ; q B = 50 q = q A + q B = (00 p) + 50 =

4 So the pro t function can be rewritten as = (fixedfee) + p(q A + q B ) (fixed cos ts) = (00 p) p 50 = p p (500) Optimal price p = 5 Consumer surplus for Type B is zero. But consumer surplus for type A is positive, CS A = 8:5 406:5 Total pro t is (75) (5) + (37:5) (5) + (406:5) 000 = 465 Simpler Example: Club pricing For the consumer: Q is the number of club visits, is the xed fee (annual membership), p is the per unit price (price per visit), m is the money spent on other goods and I is the income. The club has a capacity K; we assume that K is large. The utility is given by the U = m+ Q: So the consumer maximizes U = m + Q subject to m + + pq I or maximizes U = I pq + Q: This gives a demand function p = p Q If the club does not charge any membership fee, = 0 : the pro t function of the club is = pq = Q p Q : The seller charges p = p K and sets Q = K: If the club does charge membership fee, > 0 : let us assume that the p = 0: So the pro t function is = subject to I + Q I(reservation utility). This implies = Q: Again since the seller will utilize the whole capacity Q = K; = K: With two part tari the seller can do better. (check gure) Peak load pricing: Let there be a monopoly airline ying on a single route, during high (H) and low (L) seasons. The demand functions are given where A H > A L > 0 p H = A H Q H p L = A L Q L Let r > 0 denote the unit capacity cost. And c denotes the operational cost. So if K is the capacity of the airline and Q H and Q L are the quantity sold in the high and low season respectively, the total cost is T C = (Q H + Q L ) c + rk K Q H ; Q H > Q L 4

5 The pro t maximizing seasonal pricing MR H (Q H ) = c + r MR L (Q L ) = c Prices are P H = A H + c + r P L = A L + c Bundling; rms o er more than one unit for sale. (of the same good) example: DVD movie packs, Studios like MGM and Fox used to bundle movies together to distributors Tying: rms o er packages of two di erent products example: Burger King whopper meal Bundling: let there be a monopolist selling in a market with demand curve Q = 4 p and assume that marginal cost is zero: With monopoly pricing, equating MR = MC we get monopoly price p M = and Q M = : There ore pro t is = 4: Now instead if the seller bundles 4 units together at a price 7:99: The monopolist makes 7:99 > 4: And for the consumer the consumer surpplus is (4) (4) 7:99 0: So the consumer will buy the bundled good. Tying: Example: Sky selling phone, broadband and digital television. Consider a monopoly selling two goods labelled X and Y: For simplicity assume that the production is cost less. And there are two consumers, and, who are willing to buy at most one unit of each good. The consumer s valuation of the goods is given by H > L X Y cons valuation = H valuation = L cons valuation = L valuation = H No tying: If the monopolist sets p X = L; p Y = L: So the pro t will be 4L: No tying: If the monopolist sets p X = H; p Y = H: So the pro t will be H 5

6 Tying: Now if the seller sets the price p X+Y = L + H; for the goods X and Y together. Both consumers will buy both goods therefore pro ts will be (L + H) : Mixed tying: Consider now three consumers and two products X Y cons valuation = 4 valuation = 0 cons valuation = 3 valuation = 3 cons 3 valuation = 0 valuation = 4 There are two possibilities under no tying p X = 3; p Y = 3 or p X = 4; p Y = 4: If it is p X = 3; p Y = 3; then the pro t earned is = : And p X = 4; p Y = 4; the pro t earned is = 8: Seller will select p X = 3; p Y = 3: Under tying there are two possibilities p X+Y = 6; or p X+Y = 4: If p X+Y = 4; the pro t of the seller will be = ; and if p X+Y = 6; the pro t of the seller will be = 6: Thus the seller will select p X+Y = 4: In case of mixed bundling, the monopolist o ers the following prices, p X+Y = 6 for X and Y together or p X = 4 for X alone and p Y = 4 for Y alone. Pro t for the seller will be = 4. Does price discrimination help or hinder competition: Price competition may increase: In case of elastic demand, the seller may want to decrease price to include new customers. Competition may su er:. Predatory discrimination: imagine Starbucks selling co ee at a lower price at Exeter than the rest of the country. This may harm the local co ee retailers. Example: Microsoft. Secondary line cases: if Ben & Jerry s sold ice cream to Tesco at a cheaper price than to Sainsbury s. This would allow Tesco to outcompete Sainsbury s. Example: Walmart. 6