2 Some economics of price discrimination

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1 1 Price discrimination Price differences are ubiquitous in the real world In-state residents and out-of-state residents pay different tuition to attend the same public university A passenger who purchases a plane ticket at the last minute pays substantially more to make the same trip than a passenger who purchases far in advance Senior citizens and students are often able to obtain discounts that are not available to those in the prime of life Prices differences alone do not make price discrimination, but prices differences for consumers who are supplied at the same marginal cost do Many prices differences reflect differences in marginal cost It is cheaper for a canned-goods manufacturer to supply a grocery store chain that buys in bulk than a mom-and-pop store that buys in small lots If the grocery store chain receives a price that is lower in proportion to the lower marginal cost of supplying the grocery store chain, the owner of the mom-and-pop store is not discriminated against Many price differences appear not to reflect differences in the marginal cost of supplying different customers As we will see, the welfare effects of price discrimination are ambiguous Yet antitrust policy has been consistently hostile to price discrimination We will try to understand why 2 Some economics of price discrimination For simplicity, we limit our discussion to price discrimination by a monopolist From the work of Pigou (1920) onward, it is customary to distinguish three types of price discrimination: (1) First degree price discrimination: each consumer pays his or her reservation price the maximum price the consumer is willing to pay for each unit of the good consumed (2) Second degree price discrimination: output is divided into successive lots, each lot being sold for the highest price at which the whole lot will be purchased (3) Third degree price discrimination: consumers can be partitioned into a number of groups; the supplier sets a profit-maximizing price for each group As Pigou remarks (1950, p 279) in real life the third degree only is found We briefly discuss first-degree price discrimination to make the point that the welfare implications of price discrimination are ambiguous 1

2 and concentrate on third-degree price discrimination 21 First-degree price discrimination Figure 1 illustrates the welfare consequences of first-degree price discrimination First-degree price discrimination permits the monopolist to wring the maximum possible profit out of the market Consumers enjoy no surplus each consumer pays his or her reservation price for every unit purchased Nor do consumers suffer a deadweight welfare loss: output is the same as it would be in long-run perfectly competitive equilibrium There is no monopolistic output restriction Price discrimination improves market performance and increases social welfare The extra profit collected by the monopolist does not come out of thin air It is consumer income that would, in the absence of price discrimination, be spent in other industries The customary assumption that is made for expositional purposes is that all other markets are perfectly competitive, so that prices in those markets equal the marginal cost of supplying those markets If this assumption holds, output reductions in other markets are valued at the marginal cost of production, while output increases in the market where price discrimination takes place are valued at more than the marginal cost of production Then the increase in output represents an overall increase in welfare, even taking reduced output in other markets into account 22 Third-degree price discrimination Prerequisites for third-degree price discrimination to occur are that consumers can be segmented into groups, and that consumer arbitrage resale from one group to another is not possible Consumer arbitrage will generally not be possible, for example, with services Impediments to consumers arbitrage may be part of product design Thus the denaturing of alcohol blocks arbitrage between the industrial consumers of alcohol and the alcoholic beverage market A prerequisite for third-degree price discrimination to be profitable is that different groups of consumers have different price-elasticities of demand We know from our review of the basic monopoly model that a monopolist s profit-maximizing price for supplying a market makes the price-marginal cost marginal equal to the inverse of the price-elasticity of demand If different 2

3 p Q 100 p m =55 c = q m =45 50 Q c =90 p Q Demand curve Marginal cost curve DWL CS DWL = deadweight welfare loss under single-price monopoly CS = consumers surplus under single-price monopoly CS + DWL = gross increase in monopoly profit under first-degree price discrimination DWL = gross increase in social welfare under first-degree price discrimination Figure 1: First-degree price discrimination, p =100 Q, marginal cost =10 3

4 200 p 1 I: p 1 = 200 2Q 1 II: p 2 =100 Q 2 D 1 p 2 D Q Q 2 Figure 2: Group demand curves 4

5 groups of consumers have different price-elasticities of demand, a monopoly supplier will find it profitable to charge them different prices p c p = 1 ε Qp (1) Figure 2 shows a pair of demand curves for two markets If the markets cannot be segmented, the two group demand curves and p 1 = 200 2Q 1 (2) p 2 =100 Q 2 (3) add up to the combined inverse demand curve with equation ½ 200 2Q 0 Q 50 p = (4) Q 50 Q The equations of the two segments of the marginal revenue curve can be derived from the equations of the two segments of the inverse demand curve, in the usual way If a monopolist with constant marginal cost 10 must supplies both groups at a single price, equilibrium values are those shown in Figure 3 If, in contrast, it is possible to segment the two groups of consumers, the monopolist will find it profitable to do so This is shown in Figure 4 The profit-maximizing monopolist will charge a higher price to group 1, and a lower price to group 2, compared with the no-price-discrimination value Figure 4 reports other price-discrimination-equilibrium values Price discrimination is profitable: with price discrimination the monopolist earns profit 6,5375, without price discrimination only 5,70417 Price discrimination also leaves consumers worse off (consumer surplus 3,26875 with price discrimination, compared with 4,51875 without) The loss of consumer surplus exceeds the gain in economic profit: net social welfare falls if there is price discrimination (9,80625 versus 10,22292) The result of this example that price discrimination is privately profitable but reduces social welfare holds when demand curves are linear If demand curves truly curve, then the welfare effects of price discrimination are ambiguous: price discrimination, in general, may increase or decrease social welfare 5

6 p Q c = p Q D 1 + D 2 p = ½ 200 2Q 0 Q Q 50 Q 200 π = CS = NSW = Marginal revenue curve Marginal cost curve Figure 3: Monopoly output, third-degree price discrimination not possible Shaded area indicates consumer surplus 6

7 p 1 Q 1 p 2 Q c =10 c = D 1 MR 1 D 2 MR 2 I: p 1 =200 2Q 1 II: p 2 =100 Q 2 π 1 =45125 CS 1 = NSW 1 = π 2 =2025 CS 2 =10125 NSW 2 =30375 π 1 + π 2 = NSW 1 + NSW 2 = Figure 4: Third-degree price discrimination Shaded areas indicate consumer surplus 7

8 200 p 1 I: p 1 =200 2Q 1 II: p 2 = 100 Q 2 D p 2 D 2 Q Q 2 Figure 5: With price discrimination, group II consumers with relatively low reservation prices purchase the good and enjoy some consumer surplus (shaded area on the right), while group I consumers with relatively high reservation prices do not purchase the good and suffer a loss of consumer surplus (shaded area on the left) 8

9 Price discrimination brings with it a source of welfare distortion that is distinct from the familiar deadweight welfare loss due to output restriction from the exercise of market power Figure 5 shows compares prices and outputs for the two groups if price discrimination is and is not possible With price discrimination, group I consumers are faced with a higher price, and some of them drop out of the market The lost consumer surplus on purchases that would have been make by group I consumer at a nondiscriminatory price is the shaded area on the left in Figure 5 Also with price discrimination, group II consumers are faced with a lower price, and some of them make purchases that would not have been made at a nondiscriminatory price The incremental consumer surplus on these sales is the shaded area on the right in Figure 5 The group I consumers who drop out of the market have higher reservation prices than the group II consumers who come into the market That consumers with lower reservation prices are able to obtain the product, while other consumers with higher reservation prices are not, is a welfare distortion due to price discrimination 3 Price Discrimination by a Monopolist Upstream monopolist produces an input that is purchased by two downstream firms The downstream firms process the input, in combination with some other inputs, to make a product that is sold to final consumers The equation of the inverse demand curve for the final good is Assume the input is produced at no cost p = 100 (q 1 + q 2 ) (5) one unit of the monopolized input is needed to produce one unit of the final good Downstream firms have marginal cost 10 and 20 per unit of final good output, respectively, and the input monopolist knows the values of these marginal costs 9

10 ω 1 = input price to downstream firm 1 ω 2 = input price to downstream firm 2 Cost functions of the downstream firms: c 1 (q 1 )=(10+ω 1 ) q 1 (6) c 2 (q 2 )=(20+ω 2 ) q 2 (7) The downstream firms compete as Cournot oligopolists The equilibrium outputs of the two downstream firms, which depend on the input prices set by the upstream monopolist, are q 1 (ω 1,ω 2 )= 1 3 (100 2ω 1 + ω 2 ) (8) and q 2 (ω 1,ω 2 )= 1 3 (70 2ω 2 + ω 1 ), (9) respectively The downstream firms purchase one unit of the input for every unit of output that they sell Derived demand for input: The upstream firm s payoff is q 1 (ω 1,ω 2 )+q 2 (ω 1,ω 2 ) (10) π u (ω 1,ω 2 )=ω 1 q 1 (ω 1,ω 2 )+ω 2 q 2 (ω 1,ω 2 ) (11) Suppose price discrimination is not permitted: the upstream firm must set one input price, ω 1 = ω 2 = ω It will pick the value of ω that maximizes π u (ω, ω) is maximized for π u (ω, ω) = 1 ω (170 2ω) (12) 3 ω = 170 =425 (13) 4 Substituting (13) into (8) and (9), the equilibrium outputs of the downstream firms are q 1 (ω, ω) = =1917 q 2 (ω, ω) = 55 =917 (14) 6 10

11 For this linear inverse demand, constant marginal cost example, each firm s downstream payoff is the square of its output Total output is for the finalgood,andtotalsalesoftheinput, = 85 =2833 (15) 3 Substituting (13) into (12), the upstream firm s payoff is π u = 7225 = (16) 6 If the upstream firm can set a different price for each of the downstream firms, the upstream firm picks ω 1 and ω 2 to maximize π u = 1 3 [ω 1 (100 2ω 1 + ω 2 )+ω 2 (70 2ω 2 + ω 1 )] (17) The profit-maximizing input prices are ω 1 =45 ω 2 =40 (18) When price discrimination is possible, the upstream firm sets a higher price for the low-cost downstream firm, and a lower price for the high-cost downstream firm In this sense, one can say that price discrimination distorts competition in the downstream market, to the advantage of the high-cost downstream firm and to the disadvantage of the low-cost downstream firm With price discrimination, the outputs of the downstream firms are q 1 (ω 1,ω 2 )= 50 3 =1667 q 2 (ω 1,ω 2 )= 35 3 =1167 (19) From this perspective as well, price discrimination disadvantages the lowcost downstream firm, which ends up producing less than it would if price discrimination were forbidden With price discrimination, the upstream firm s payoff is µ µ π u = = 3650 = , (20) and this is greater than its payoff if it cannot price discriminate, (16) 11

12 Thus price discrimination leaves the upstream better off, the low-cost downstream firm worse off, and the high-cost downstream firm better off But total output is the same with or without price discrimination: from (19), with price discrimination, total output is = 85 3, (21) which is the same as (15) Since price discrimination does not change total output, it does not change the price consumers pay for the final good, and it does not change consumer surplus 4 Price Discrimination to Support Collusion Two producers of the upstream good They produce identical versions of the input They compete as price-setting duopolists There are n firms in the downstream market They produce identical versions of the final good One unit of the input is needed to produce one unit of the final good The constant marginal and average cost of the downstream firms for all inputs except the one produced by the upstream firms is c per unit The downstream firms also compete as price-setting oligopolists Find the equation of the derived inverse demand curve facing the upstream firms The equation of the inverse final demand curve is p =100 Q (22) ω = the input price Marginal cost of the downstream firms, taking all inputs into account, is c + ω (23) The equilibrium price is marginal cost; in equilibrium, c + ω =100 Q, (24) so that the equation of the derived inverse demand curve for the upstream good is ω =100 c U, (25) 12

13 (where U = Q is the quantity demanded of the upstream good) Since the upstream firms compete by setting prices, the equilibrium input price equals the marginal cost of producing the upstream good, ω B =0 The equilibrium price in the final good market is p B = c Upstream and downstream firms earn zero economic profits What if the upstream firms collude and obtain monopoly profit? Monopoly output for the inverse demand curve (25) is which makes the monopoly input price U m = 1 (100 c), (26) 2 ω m =100 c 1 2 (100 c) =1 (100 c) (27) 2 Monopoly profit would be π m = 1 4 (100 c)2 (28) Onewaytoreachthisoutcome: The upstream firms, U 1 and U 2, set the monopoly price ω m = 1 (100 c) 2 for all downstream firms except the first, D 1 D 1, publicly or privately, is quoted the price ω 1 = 1 3 (100 c) <ω m (29) The downstream market is a price-setting oligopoly D 1 can undersell his rivals slightly and drive them out of business D 1 will set a price slightly less than ω m and sell a quantity of the final good slightly greater than Q m = U m 13

14 As its contribution to the collusive scheme, D 1 buys half its inputs from U 1 and half its inputs from U 2 Leaving aside the small discrepancy due to the fact that D 1 sets a price just below c + ω m,eachofthethreefirms (U 1, U 2,andD 1 ), collects profit per period 1 12 (100 c)2 (30) The three firms split the monopoly profit The price ω 1 has been chosen in this example to result in equal division of the monopoly profit In practice one would expect the division of collusive profit to depend on a bargaining process Here, as in the earlier example, price discrimination distorts competition in the downstream market Here, however, price discrimination worsens market performance and reduces consumer welfare The examples of the two sections together suggest that the answer to the question Does price discrimination in the present circumstance distort competition? may be a poor guide to theanswerofthequestion Doesprice discrimination in the present circumstance worsen market performance? 14