# Sustainability in a multiproduct context Competition Policy and Market Regulation MEFI – Università di Pavia.

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Sustainability in a multiproduct context Competition Policy and Market Regulation MEFI – Università di Pavia

Properties of a sustainable allocation (multiproduct context and contestable markets) If a sustainable allocation exists it has the following properties: 1.A single firm takes advantage of cost sub-additivity 2.The firms earns zero profits (break-even) 3.No cross-subsidization (the price charged for any product or subset of products covers the incremental cost) 4.The price of each product (subset of products) is greater than MC 5.The firm may voluntary charge the second best linear prices (P = AC in the single product case) Sub-additivity of the multiproduct cost function does not assure that a sustainable zero-profit (break-even) configuration exists

Sustainable configurations and sustainable tariffs: a multiproduct example Case of local transports: 3 towns (or areas of one city) are linked with a bus service 3 markets: a, b, c The demand of transport services is inelastic to price: D(P) =1 Cost Function: C(a) = C(b) = C(c ) = 10 C(a, b) = C (b, c) = C (a, c) = 18 C( a, b, c) = 24 a bc Sub-additive cost function

Sustainable tariffs Cost Recovery Non-profitable Entry in one ore more markets Prices not greater than stand-alone cost P a 10, P b 10, P c 10 P a + P b 18, P a + P c 18, P b + P c 18 P a + P b + P c = 18 P i V i for any i (willingness to pay) V a = V b = V c = 11

Solutions One sustainable configuration is: P a = P b = P c = 8 A non-sustainable configuration: P a 18

Case for a non-sustainable configuration P a 18 Letsuppose V c = 5, then set P c = 5 implying P a = P b = 9.5 (to get P a + P b + P c = C(abc)= 24) 1.Market C is subsidized by A and B 2.P a + P b = 19 > 18 = C(ab): stand-alone cost 3.Entry becomes possible in markets b and c, with prices P a = P b = 9,5 – ε Cream Skimming 4.Non sustainable natural monopoly: monopoly is feasible if coupled with legal barriers to entry

Should we supply transport services to market C? Efficiency and Social Issues Remember: V c = 5 while V a = V b = 11 Efficiency criteria maximization of net total benefit: 1.Supply all markets: ( V a + V b + V c ) – C (abc) = 27 -24 = 3 2.Supply only markets a and b:( V a + V b ) – C(ab) = 22- 18 = 4 Efficiency criteria do not justify transport links to market C

Should we supply transport services to market C? Efficiency and Social Issues Letintroduce equity issues (social protection of consumers in market C) For example: universal service obligation Transport services supplied to market C may be justified on this ground But then cross-subsidies are required, leading to entry and cream skimming which reduces the revenues of the incumbent in market b and c To avoid entry - and preserve monopoly - legal barriers to entry are required

General conditions for sustainable tariffs (pricing without cross-subsidies) N markets supplied by a monopolist S: subset of the N markets C(S) = minimum cost of supplying S separately from the other subset of markets (N/S), known as STAND ALONE COST 1. iS p i C(S) (prices should not exceed Stand Alone costs) 2. iN p i = C(N) (break-even constraint)

General conditions for sustainable tariffs (pricing without cross-subsidies) N/S complementary subset of markets Cost recovery requires: iN p i = iN/S p i + iS p i = C(N) To get: iS p i = C(N) - iN/S p i As we require: iN/S p i C(N/S) We obtain: iS p i C(N) - C(N/S) In each submarket Prices should not be lower than incremental costs

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