Third degree price discrimination Welfare Analysis

Third-degree price 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

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,  p=2,  2.Discrimination: p a =2, p b =4,   Less consumers are served

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,  p=2,  2.Discrimination: p a =4, p b =2,  Total output increases More consumers served

Price discrimination and welfare Suppose that there are two markets: “weak” and “strong” D1D1 MR 1 D2D2 MR 2 MC P1P1 P2P2 ΔQ1ΔQ1 ΔQ2ΔQ2 Price Quantity PUPU PUPU The discriminatory price in the weak market is P 1 The discriminatory price in the strong market is P 2 The uniform price in both market is P U G The maximum gain in surplus in the weak market is G L The minimum loss of surplus in the strong market is L

Price discrimination and welfare D1D1 MR 1 D2D2 MR 2 MC P1P1 P2P2 ΔQ1ΔQ1 ΔQ2ΔQ2 Price Quantity PUPU PUPU GL It follows that ΔW < G – L= (P U – MC)ΔQ 1 + (P U – MC)ΔQ 2 = (P U – MC)(ΔQ 1 + ΔQ 2 ) Price discrimination cannot increase surplus unless it increases aggregate output Price discrimination cannot increase surplus unless it increases aggregate output

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

New markets: an example Demand in “North” is P N = 100 – Q N ; in “South” is P S = 100  - Q S $/unit NorthSouthAggregate Quantity  Marginal cost to supply either market is $20 MC Demand MR

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

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

The example again Previous illustration is too extreme So there are potentially two equilibria with uniform pricing MC cuts MR at two points Quantity $/unit Aggregate MC Demand MR At Q 1 only North is served at the monopoly price in North Q1Q1 PNPN At Q 2 both markets are served at the uniform price P U Q2Q2 PUPU 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 MC “high enough” serve only North

Price discrimination and welfare (cont.) Quantity $/unitAggregate MC Demand MR Q1Q1 PNPN In this case only North is served with uniform pricing But MC is less than the reservation price P R in South PRPR So price discrimination will lead to South being supplied Price discrimination leaves surplus unchanged in North But price discrimination generates profit and consumer surplus in South So price discrimination increases welfare

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.