Tham khảo tài liệu 'the free information society bargaining and markets_5', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Analysis of Model A 127 and i S0 B0 1 - p 1 - S0 B0 SVb if p 0 1 V 1ỖVb if p D. The first part of the definition requires that the agreement reached by the agents be given by the Nash solution. The second part defines the numbers Vi i s b . If p is a price then Vs p since a seller is matched with probability one and Vb S0 B0 1 p 1 S0 B0 ỖVb since a buyer in period t is matched with probability S0 B0 and otherwise stays in the market until period t 1 . The definition for the case B0 S0 is symmetric. The following result gives the unique market equilibrium of Model A. Proposition If Ỗ 1 then there is a unique market equilibrium p in Model A. In this equilibrium agreement is reached and 9 _ Ỗ Ỗo R if B0 - S0 2 Ỗ ỖS0 B0 p 1 11 2 B - B s . Proof. We deal only with the case B0 S0 the other case is symmetric . If p D then by and we have Vs Vb 0. But then agreement must be reached. The rest follows from substituting the values of Vs and Vb given by and into . The equilibrium price p has the following properties. An increase in S0 B0 decreases p . As the traders become more impatient the discount factor Ỗ decreases p moves toward 1 2. The limit of p as Ỗ 1 is B0 S0 B0 . Note that if Ỗ is equal to 1 then every price in 0 1 is a market equilibrium. The primitives of the model are the numbers of buyers and sellers in the market. Alternatively we can take the probabilities of buyers and sellers being matched as the primitives. If B0 S0 then the probability of being matched is one for a seller and S0 B0 for a buyer. If we let these probabilities be the arbitrary numbers Ơ for a seller and p for a buyer the same in every period we need to modify the definition of a market equilibrium and must be replaced by Vs ơp 1 ơ ỖVs Vb p 1 p 1 P ỖVb. In this case the limit of the unique equilibrium price as Ỗ 1 is ơ ơ p . 128 Chapter 6. A First Approach Using the Nash Solution The constraint that the equilibrium price not depend on time is not .
