# Third degree price discrimination Welfare Analysis Thirddegree price

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Third degree price discrimination Welfare Analysis

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

Example 1 – Welfare decreases Two markets q Market A: n n n q Market B: n n n q All identical Na=100 consumers Reservation value pa=2 1. No discrimination: 2. p=4, p=(41)*50=150 3. 200 p=2, p=(2 -1)*200 = 2. Discrimination: 3. pa=2, pb=4, p=100+150 Two types. N 1 =N 2 = 50 of each 4. Less consumers are Reservation values p 1 =4, p 2 = served 2. Constant mg. cost c=1.

Example 2 – Welfare increases Two markets q Market A: n n n q No discrimination: 2. p=4, p=(41)*120=360 2. Discrimination: All identical Na=100 consumers 3. p=2, p=(2 -1)*200 Reservation value pa=4 =200 Market B: n 1. Two types. N 1 =20, N 2 = 80. Reservation values p 1 =4, p 2 = 2. Constant mg. cost c=1. pa=4, pb=2, p=300+100 • Total output increases • More consumers served

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

Price discrimination and welfare Price D 1 Price discrimination cannot increase surplus unless it increases aggregate output PU Price D 2 MR 2 PU P 1 MR 1 G L MC ΔQ 1 Quantity MC ΔQ 2 Quantity It follows that ΔW < G – L = (PU – MC)ΔQ 1 + (PU – MC)ΔQ 2 = (PU – MC)(ΔQ 1 + ΔQ 2)

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

New markets: an example Demand in “North” is PN = 100 – QN ; in “South” is PS = 100 - QS Marginal cost to supply either market is \$20 North South \$/unit Aggregate \$/unit 100 Demand MC MC MC MR Quantity

The example: continued Aggregate demand is P = (1 + )50 – Q/2 provided that both markets are served \$/unit Aggregate Equate MR and MC to get equilibrium output QA = (1 + )50 - 20 Get equilibrium price from aggregate demand P = 35 + 25 P Demand MC MR QA Quantity

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

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

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

Price discrimination and welfare again n n Suppose only North is served with a uniform price Also assume that South will be served with price discrimination q q q n 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.