handoutsearch - A Primer on Search Models of Money Based on...

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A Primer on Search Models of Money Based on Trejos and Wright (1995) “Search, Bargaining, Money, and Prices”, Journal of Political Economy, p.118-39. 1 Environment Unit measure of agents. Pref: each agent has preferences over a variety of goods that can be pro- duced by a fraction x of the population. q units consumed generates utility u ( q ) Tech: each agent can produce q units of one nonstorable good at cost cq . Thegoodisdemandedbyfract ion x of the pop. E cient quantity is u 0 ( q )= c (i.e. MB=MC). Fraction M of the population are endowed with 1 unit of indivisible money. Inventory is bounded above by 1 . Matching technology: It any given period the probability of matching with another agent is β. Given above: arrival rate of an appropriate buyer for a seller is βMx (meet agent with money who likes my good) ” seller for a buyer is β (1 M ) x Normalize βx =1 . Bargaining Protocol When an appropriate buyer and seller meet, they bargain over q (the amount of good to be traded for a unit of money p = 1 q ). In 1st generation models, q ,so p = 1 independent of M . Nash bargaining. Can be formalized as a sequential game between the buyer and seller a la Rubinstein (1982, Ecta). 2 Steady State Equilibrium in the Trejos-Wright Model In 3 parts: 1. taking prices as given (i.e. q t = Q t ), determine the value of being a buyer V bt ( Q t ) or a seller V st ( Q t ) .
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handoutsearch - A Primer on Search Models of Money Based on...

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