1 Bargaining & Markets u Two populations: Buyers and Sellers u A sellers has 1 indivisible unit to sell u A Buyer has 1 unit of divisible money u If they agree on a price at period t, their utilities are: δ t p, δ t (1-p). u Random matching of pairs (buyer & seller) u Bargaining breaks down after 1 period, if there was no agreement

2 Bargaining & Markets u The Populations: Continuous or finite sets B, S u Bargaining: Nash Bargaining Solution, with the expected continuation values δV S, δV B as the disagreement point. u A pair that reached agreement leaves the market u Matching: If B > S then all sellers are matched and a buyer is matched with probability S/B.

3 Bargaining & Markets Model 1: The populations sizes B, S do not change with time. i.e. new individuals enter the market to replace those that left. ( Assume B > S ) We seek an equilibrium in stationary and anonymous strategies

4 Bargaining & Markets Model 1: B, S constant

5 Bargaining & Markets Model 1: B, S constant

6 Bargaining & Markets Model 1: B, S constant

7 Bargaining & Markets Model 1: B, S constant

8 Bargaining & Markets Model 1: B, S constant

9 Bargaining & Markets Model 1: B, S constant

10 Bargaining & Markets Model 1: B, S constant

11 Bargaining & Markets Model 1: B, S constant Find p when S >B !!!!

12 Bargaining & Markets Model 1: B, S constant q p S 1 B Supply Demand Microeconomics I ?? p = 1

13 Bargaining & Markets Model 2: No new individuals enter the market. The populations shrink over time. Let the initial populations be of sizes B 0, S0.S0. Since equal numbers of buyers & sellers leave the market, the populations B,S at any period satisfy: B -S = B0 B0 - S0.S0. ( Assume B0 B0 > S0 S0 )

14 Bargaining & Markets Model 2: No new entry If there is agreement then all pairs leave and only B0 B0 - S 0 buyers remain. If there is agreement and one pair deviates then there will remain B 0 - S 0 +1 buyers and 1 seller in the market The disagreement point for all pairs is:

15 Bargaining & Markets Model 2: No new entry

16 Bargaining & Markets Model 2: No new entry

17 Bargaining & Markets Model 2: No new entry

18 Bargaining & Markets Model 2: No new entry

19 Bargaining & Markets Model 2: No new entry Find p* when S >B !!!!

20 Bargaining & Markets Justifying the assumptions of Models 1 & 2 The Market Model 1 or 2 Individuals born each period

21 Bargaining & Markets Model 1 (constant populations) Equal numbers of buyers & sellers should enter each period The Market Model 1 Individuals born each period

22 Bargaining & Markets Justifying Model 1

23 Bargaining & Markets Justifying Model 1

24 Bargaining & Markets Justifying Model 1

25 Bargaining & Markets Justifying Model 1

26 Bargaining & Markets Justifying Model 2 Entry has a large effect on prices Assume that an entrant anticipates his effect on prices ?

27 Bargaining & Markets Justifying Model 2 Assume that an entrant anticipates his effect on prices ?

28 Bargaining & Markets Justifying Model 2 Topics -5