# Price Discrimination: Part 1

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1 Price Discrimination: Part 1 Sotiris Georganas January 2010

2 \The textbook monopolist is a wasteful agent." 1 Pricing tactics Pigou's (1920) taxonomy of price discrimination: { First-degree (or perfect) price discrimination: The producer discriminates across sold units and consumers captures the whole consumer surplus. { Second-degree price discrimination:

3 Per-unit prices of the good dier, but these prices are the same for all consumers (e.g., quantity discounts). { Third-degree price discrimination: Per-unit prices of the good are the same for a given consumer, but dierent consumers pay dierent prices (e.g., student discounts). Commodity bundling

4 2 Price discrimination Denition 1 A producer price-discriminates when two units of the same physical good is sold at dierent prices, either to the same consumer or to dierent consumers. Note that the denition includes the quantity discount case (\buy 3 pay for 2"). The possibility of price discrimination is closely linked to the possibility of arbitrage.

5 2.1 Arbitrage Transferability of the commodity (between consumers). Transferability of demand (between oered bundles).

6 3 Perfect price discrimination (1st degree) The monopolist succeeds in capturing the entire consumer surplus. Version 1 Each consumer demands one unit of the monopolist good, Consumer i's willingness to pay for the good is v i : The monopolist observes v i and oers to sell a unit of the good to consumer i at the (individual) price p i = v i, leaving the consumer just indierent.

7 Version 2 Assume there are a large number of identical consumers with downward sloping demand curves. Assume that the monopolist has a constant marginal cost c. (Fig. 1) 1. The monopolist can make a take-it-or-leave-it oer to sell q c units to consumer i at the total price A + B: The consumer is just willing to accept. or

8 2. The monopolist can set an access charge of A and then charge the price p c = c for each unit sold. The consumer accepts to pay the access charge and buys q c units. Perfect price discrimination gives the maximum possible prots to the monopolist, but it also requires a lot of information; he has to know the individual demands, and he must be able to prevent resale of the good Examples?

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10 4 Multimarket price discrimination (3rd degree) Multimarket price discrimination refers to a situation where the monopolist can divide the market into m groups (or market segments) on the basis of some observed information and can charge a dierent prices to the dierent groups. Requires that arbitrage between the groups is not possible.

11 4.1 Analysis Assume { two market segments with inverse demands equal to p 1 (q 1 ) and p 2 (q 2 ) respectively. { The rm has a general cost function C (q 1 + q 2 ), where q i is the amount sold in market i, i = 1; 2. The rm solve maximizes the total prots from the two market segments. max q 1 ;q 2 fp 1 (q 1 ) q 1 + p 2 (q 2 ) q 2 C (q 1 + q 2 )g :

12 The optimal solution involves setting the marginal revenue in each market segment equal to the marginal cost: MR 1 (q 1 ) p 1 (q 1 ) + p 0 1 (q 1) q 1 = C 0 (q 1 + q 2 ) ; MR 2 (q 2 ) p 2 (q 2 ) + p 0 2 (q 2) q 2 = C 0 (q 1 + q 2 ) : Note that this implies that MR 1 (q 1 ) = MR 2 (q 2 ).

13 Note also that the marginal revenue can be expressed in terms of the demand elasticity where MR i (q i ) = p i (q i ) + p 0 i (q i) q i = p i (q i ) = p i (q i ) " " 1 + p 0 i (q i) 1 " i (p i ) = dq i dp i p i q i : 1 j" i (q i )j q i p i (q i ) # : #

14 But then MR 1 (q 1 ) = MR 2 (q 2 ) implies that, across the two markets, # " # 1 1 p 1 "1 = p 2 1 ; j" 1 j j" 2 j from which it follows that the monopolist sets a higher price in the market segment with least price elastic (sensitive) demand: p 1 > p 2, j" 1 j < j" 2 j. Intuitively, if there two groups of beer consumers, heavy drinking guys and their female companions, the monopolist will charge the guys more (does this explain ladies' nights?)

15 5 Spot the discrimination Concert ticket price below equilibrium level Disneyland (entry fee + prices per ride) Bulk discounts in supermarket Student or senior prices for books, travel etc Cable or phone compay pricing packages Dierent prices for lunch or dinner at same restaurant

16 6 Welfare aspects of perfect- and multimarket price discrimination Perfect price discrimination Perfect price discrimination leads to an ecient allocation (the good is produced whenever the marginal willingness to pay exceeds the marginal cost). It does, however, have distributional eects (prots rather than consumer surplus).

17 Multi-market price discrimination Multi-market discrimination increases the monopolist's prots; however, the impact on aggregate eciency is not clear. Does multi-market price discrimination lead to a more ecient allocation than non-discrimination? Sources of ineciency under multi-market price discrimination: 1. Output ineciency: price exceeding marginal cost implies \too low output". 2. Consumption ineciency: Since consumer pay dierent prices, each consumer's marginal willingness to pay is not the same.

18 If the monopolist does not discriminate, then only the rst source of ineciency is present, but this source may then be more severe. Figs. 2 and 3. The discriminating monopolist sets a price p 1 in market 1 and price p 2 in market 2: This causes a total deadweight loss equal to the sum of B and C: The non-discriminating monopolist sets a (single) price p and causes a deadweight loss equal to A: We cannot unambiguously say which deadweight loss (B + C or A) is larger.

19 General rules of thumb: { If discrimination increases total output, then discrimination may be good for eciency. { If non-discrimination leads to a price such that some group does not buy at all, then discrimination may be good. { The closer imperfect price discrimination is to perfect price discrimination, the more likely it is that price-discrimination leads to a more ecient outcome. In other words, the better the signal allows the monopolist to sort consumers, the more likely it is that price-discrimination is good for eciency.

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22 7 Screening: Introduction Suppose that the monopolist does not receive any signal of the consumer's demand (i.e. he cannot observe age etc.); he cannot tell the consumers apart he only knows that there is heterogenous demand. Does this mean that the monopolist cannot do better than to charge a single price to all? The answer is in general no { provided that arbitrage can be prevented. So what can he do? He can:

23 { Oer a menu of bundles to choose from. { Take into account the possibility of \personal arbitrage". This will typically involve quantity-discounts. next lecture... But we leave this for

24 8 What to remember from this lecture What is price discrimination. How arbitrage can limit the scope for price discrimination. Forms of perfect price discrimination. Multimarket price discrimination and the inverse elasticity rule. Eciency aspects of perfect and multimarket price discrimination. The problem of screening and the transferability of demand.

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