Third Degree. Distinguish from First-Degree or Perfect Price Discrimation

Transcription

1 Third Degree Distinguish from First-Degree or Perfect Price Discrimation Large literature from Pigou (1920) and Robinson (1933) to AER today (Aguirre, Cowan and Vickers, Sept 2010 AER, Monopoly Price Discrimination and Demand Curvature ) Large question relates to the first welfare theorem. With uniform price monopoly we don t get efficiency. Perfectly discriminating monopoly we get efficiency. What happens in between, closer to efficiency? Illustate Pigou s point with liner demand on the board.

2 Get output issue in general as well as a distortion: goods not allocated to consumers with highest willingness to pay. Is this empirically important?

3 Stole Handbook version of Holmes (1989) Two markets =1 2, duopolists =. ( )demandoffirm in market given prices (assume syjmetric) Market demand ( ) = ( ) = ( ) and market elasticity ( ) = ( ) 0 ( ) Firm 0 elasticity of demand in market, ( )= ( ) ( )

4 which at symmetric prices = = is ( ) = ( ) 0 ( )+ ( ) ( ) = ( )+ ( ) where ( ) 0 is the cross-price elasticity of demand at symmeric prices Monopoly pricing rule: = 1 ( ) Bertrand duopoly pricing: = 1 ( )+ ( ) Can see two reasons for price discrimination in oligopoly.

5 Output and Welfare Effects Do determine effects, take two markets where 1 2 with discrimation and compare what happens with constraint = 1 = 2. Consider following procedure, assume firms have constraint 2 = 1 + (so price difference is limited by arbitrage. So symmetric FONC given is 1 ( 1)+( 1 ) 1 ( 1 1 ) + 2 ( 1 + )+( 1 + ) 2 ( ) = 0

6 ( ) = 1 ( 1 ( )) + 2( 1 ( )+ = 0 is uniform pricing. So ( ) increasingin implies aggregate output increases from price discrimination. The condition that 0 ( ) 0canbeshowntobeequivalentto the condition

7 Comments... Figure 1:

8 Lecture on Hendel and Nevo Intertemporal Price Discrimation in Storable Goods Markets Motivating Facts Look firstatpricefluctions (Fig 1) How do consumers behave (Table 1). Evidence for dynamics, storage, heterogeneity,... Model model of pricing setting delivers such behavior? Search?

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11 Loss leaders? Intertemporal Price Discrimination?

12 General Model of Demand and Supply with Storable Products Consumer at time has utility ( : )= ( ) vector of quantities of different goods money time varying preference shock Vector of purchases Inventory

13 Consumer problem max X =0 + ( + + ) ( + such that and + =

14 Seller s monopoly problem max X =0 ( ( + ) )= X =0 h ( + + ) 0 + ( + + ) i where is history (Note sure where price discrimination is showing up in this problem. More generally have different consumers and have to maximize profit on the sum of the consumers. Player strategies? Buyers current behavior depends upon inventories. sellers probably can t get too far in pricing based on inventory (loyalty cards probably won t do trick) How about work with model where obserable past prices are enough to infer inventories. On top of that, this paper

15 Add differentiated products Consumption and quantity stored depend upon price non-deterministic demand

16 Simple Model A1: fraction of consumers who do not store. ( ) and ( ) utilities of the two types, both quasilinear, i.e. ( ) = ( )+ Absence storage = ( )and = ( ) A2 Storage. Free, but inventory lasts for only periods A3 perfect forsight periods ahead. A3 alternative to A3 is rational expectations

17 Purchasing Patterns Aggrgate purchases ( + )= ( )+ ( + ) Note historical prices tell us the inventory Problem of Storers X =0 0 + max X =0 X =0 ( ( )+ ) subject to and + 1 X =0 where include unused units that expire. along equilibrium path) ( ) (Won t happen

18 Effective price where =min{ } =minn o Problem of storing consumer (part about budget constraint looks sloppy, there is a shador price of spending,... max X =0 Maybe like this? ( ( )+ ) subject to ³ 0 + max X =0 µ ( ) ³ 0 Note intertemporal price connections of goods.

19 What about ties? Assume threshold such that then buy first time, but if but last opportunity.

20 Predicted Behavior Define where +1,, if +1 Assumptions A1-A3 give demand function Rational expectations define period as when buy for future consumption, have cutoff So stil can do notation If more than one product storable then have issue

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23 Much easier if have two prices, and. Suppose Coke on sale, Pepsi not. Have to decide how much Coke, to purchase knowing Pepsi s price at 1+1 may end up at one of two different levels. Decide: (Cokepurchaseofconsumptionat +1 Pepsi at +1ifonsaleat +1, Pepsi consumption (whynotwaitandfind out if drink more Pepsi tomorrow, then mightwantlesscoke?

24 Seller Third-degree price discrimination =argmax( ) ( ) Uniform pricing =max³ ( )+ ( ))( let be the solution Two period problem ( ) = ³ ( )+2 ( )( + ( )( ) If ( ) 2 then get cycles.

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26 Duopoly

27 Identification

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