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rw - Chapter 7 Search and Bargaining Models of Exchange 7.1...

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Chapter 7 Search and Bargaining Models of Exchange 7.1 Introduction In this chapter we consider models of the exchange process where, as in the previous chapter, once agents meet they exchange and part company (they do not form enduring relationships); but we now generalize things so that the rate at which they exchange is determined by bilateral bargaining. We take for granted that the reader understands the relation between strategic bargaining models and the Nash solution, as detailed in the Appendix, and already used in other chapters. We less interested here in this issue than in showing how the models can be used to address substantive questions. In Section 2, we begin with a model due to Rubinstein and Wolinsky (1985), in which there are large numbers of homogeneous buyers and homo- geneous sellers who meet at random and trade according to terms given by bargaining theory. They constructed this model in order to contrast the pre- dictions of competitive (Walrasian) equilibrium theory with the predictions of a model with explicit frictions and price setting. They argue that standard competitive equilibrium theory is useful to the extent that it provides a good approximation to more “reasonable micromechanisms” describing the trad- 1
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ing process. That is, if the real world is characterized by real frictions, then competitive theory is a useful description to the real world if it generates similar outcomes when the frictions are not too big. As frictions vanish the unique equilibrium of the Rubinstein-Wolinsky model converges to something that does not generally coincide with a Wal- rasian equilibrium of a simple static model with demand and supply de…ned using the steady state numbers of buyers and sellers in the market. Hence, Rubinstein and Wolinsky conclude that models with small frictions are not Walrasian. However, this is not the last word on the matter. In Section 3, we consider a version of a model due to Gale (1987) that, in a sense, implies the opposite conclusion. First, we generalize the Rubinstein-Wolinsky model to allow heterogene- ity. Equilibrium in his model generally involves a price distribution, with, for example, high valuation buyers paying higher prices. As the frictions vanish, the price distribution collapses to a point, consistent with competitive the- ory. 1 This could not be observed in the Rubinstein-Wolinsky model, since with homogeneous buyers and sellers the equilibrium never yields a nonde- generate price distribution. However, the limiting price is again di¤erent from the prediction of a simple static Walrasian model where demand and supply are de…ned using set of agents in the market in steady state, just as Rubinstein and Wolinsky found in their special case. What is one to make of this? Our view is that it is not very informative to compare the predictions of a static Walrasian model with those of a dynamic model, even as the frictions vanish in the latter. In particular, the set of buyers and sellers in the dynamic model is not the same as the set one
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