Third degree price discrimination. Welfare Analysis

Transcription

1 Third degree price discrimination Welfare Analysis

2 Third-degree rice discrimination and welfare Does third-degree price discrimination reduce welfare? not the same as being fair relates solely to efficiency so consider impact on total surplus

3 Example 1 Welfare decreases Two markets Market A: All identical N a =100 consumers Reservation value p a =2 Market B: Two types. N 1 =N 2 = 50 of each Reservation values p 1 =4, p 2 = 2. Constant mg. cost c=1. 1. No discrimination: p=4, π=(4 1) 50=150 p=2, π=(2 1) 200 = Discrimination: p a =2, p b =4, π= Less consumers are served

4 Example 2 Welfare increases Two markets Market A: All identical N a =100 consumers Reservation value p a =4 Market B: Two types. N 1 =20, N 2 = 80. Reservation values p 1 =4, p 2 = 2. Constant mg. cost c=1. 1. No discrimination: p=4, π=(4 1) 120=360 p=2, π=(2 1) 200 = Discrimination: p a =4, p b =2, π= Total output increases More consumers served

5 Price discrimination and welfare Suppose that there are two markets: weak and strong Price The discriminatory price in the weak market is P 1 Price The discriminatory price in the strong market is P 2 D 1 The maximum gain in surplus in the weak market is G The uniform price in both market is P U P 2 MR 2 D 2 The minimum loss of surplus in the strong market is L P U P U P 1 G L MR 1 Q 1 Q 2

6 Price discrimination and welfare Price D 1 Price Price discrimination cannot cannot increase surplus surplus unless unless it it increases aggregate output output Price P 2 MR 2 D 2 P U P U P 1 G MR 1 L Q 1 Q 2 It follows that W < G L = (P U ) Q 1 + (P U ) Q 2 = (P U )( Q 1 + Q 2 )

7 Price discrimination and welfare (cont.) Previous analysis assumes that the same markets are served with and without price discrimination This may not be true uniform price is affected by demand in weak markets firm may then prefer not to serve such markets without price discrimination price discrimination may open up weak markets In the two market case, if price discrimination opens one market, welfare always increases: In the only market that was originally served, price and quantity don t change (why?) The previously excluded market is now served

8 New markets: an example Demand in North is P N = 100 Q N ; in South is P S = 100α - Q S Marginal cost to supply either market is $20 North South Aggregate $/unit $/unit $/unit α Demand MR

9 The example: continued Aggregate demand is P = (1 + α)50 Q/2 provided that both markets are served $/unit Aggregate Equate MR and to get equilibrium output Q A = (1 + α)50-20 Get equilibrium price from aggregate demand P = α P Demand Q A MR

10 The example: continued Now consider the impact of a reduction in α $/unit Aggregate Aggregate demand changes Marginal revenue changes It is no longer the case that both markets are served P N Demand The South market is dropped Price in North is the monopoly price for that market MR MR' D'

11 The example again Previous illustration is too extreme cuts MR at two points $/unit Aggregate So there are potentially two equilibria with uniform pricing At Q 1 only North is served at the monopoly price in North At Q 2 both markets are served at the uniform price P U P N P U Demand Switch from Q 1 to Q 2 : decreases profit by the red area increases profit by the blue area MR If South demand is low enough or high enough serve only North Q 1 Q 2

12 Price discrimination and welfare (cont.) In this case only North is served with uniform pricing $/unit Aggregate But is less than the reservation price P R in South So price discrimination will lead to South being supplied P N P R Price discrimination leaves surplus unchanged in North Demand But price discrimination generates profit and consumer surplus in South So price discrimination increases welfare Q 1 MR

13 Price discrimination and welfare again Suppose only North is served with a uniform price Also assume that South will be served with price discrimination Welfare in North is unaffected Consumer surplus is created in South: opening of a new market Profit is generated in South: otherwise the market is not opened As a result price discrimination increases welfare.