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A Market with Frictions in the Matching Process: An Experimental Study

A Market with Frictions in the Matching Process: An Experimental Study. Cason and Noussair. Outlines. Introduction BWS Model Montgomery Model Comparison of the two models Experiments Setting Results Presenter’s commentaries. Introduction.

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A Market with Frictions in the Matching Process: An Experimental Study

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  1. A Market with Frictions in the Matching Process: An Experimental Study Cason and Noussair

  2. Outlines • Introduction • BWS Model • Montgomery Model • Comparison of the two models • Experiments Setting • Results • Presenter’s commentaries

  3. Introduction • Burdett, Shi and Wright (2001): directed search model with frictions (BSW model) • Montgomery (1991): search-theoretic explanation of interindustry wage differentials • Cason and Noussair (2007): experimental paper testing the above two directed search models

  4. BSW Model: The Framework • m sellers each want to sell one unit of indivisible good • n buyers each want to buy one unit of good • Stage 1: Sellers post prices p simultaneously and independently • Stage 2: Observing seller’s posted prices, buyers choose to go to one seller • Stage 3: Seller visited by one or more buyers sells the good at posted price p, obtains utility p; when more than one buyers visit a seller, the seller randomly chooses a buyer to sell the good; the buyer who gets the good obtains utility 1-p, and buyers without successful purchase obtain utility 0.

  5. BSW Model: Symmetric Equilibrium • Consider symmetric equilibrium in which sellers post the same price p and buyers go to each seller with the same probability 1/m • To get equilibrium price, we analyze backward. • =Probability that at least one buyer visits a particular seller when all buyers visit him with the same probability , then • =Probability that a given buyer gets served when he visits this seller (conditional probability)

  6. BSW Model: Symmetric Equilibrium • Suppose every seller is posting p, and one contemplates deviating to . • =probability that any given buyer visits the deviant, then probability that the buyer visits a nondeviant is • A buyer who visits a nondeviant gets served with probability • A buyer who visits a nondeviant gets served with probability

  7. BSW Model: Symmetric Equilibrium • In a symmetric equilibrium, byers must be indifferent between the deviant and any other seller. Hence we have • The expected profit of the deviant is • Constrained Maximization Problem: • Note that are both functions of .

  8. BSW Model: Symmetric Equilibrium • In equilibrium, we have . Combining this with FOC, we obtain equilibrium price • Expected number of sales (equilibrium matching function)

  9. BSW Model: Limiting Case of Large Market • Note that when we keep (market tightness) constant, as the market size grows large, the binomial distribution of the number of buyers visiting a seller change to a Poisson distribution with as the arrival rate, and the equilibrium price becomes • where we have used and hence

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