Baye Morgan Scholten (2006) - Information Search and Price Dispersion

• This page is part of a series under PHDBA279B

Introduction

Baye et al. (2006) provides a survey of models of search and clearing-house that exhibit price dispersion. The survey is undertaken through two specializable frameworks, one for search and one for cleaning-houses, which are then adapted to show the key results from the literature. There are a number of equivalent results across the two frameworks.

Search Theoretic Models of Price Dispersion

The general framework used through-out is as follows:

A continuum of price-setting firms with unit measure compete selling an homogenous product
A mass [math]\mu[/math] is interested in purchasing the product
Consumers have quasi-linear utility [math]u(q) + y[/math] where [math]y\,[/math] is a numeraire good
The indirect utility of consumers is [math]V(p,M) = v(p) + M\,[/math]
where [math]v(\cdot)\,[/math] in nonincreasing in [math]p\,[/math], and [math]M\,[/math] is income.
By Roy's identity:
[math]q(p) \equiv -v'(p)\,[/math]. 
There is a search cost [math]c\,[/math] per price quote
The customer purchases after [math]n\,[/math] price quotes
The final indirect utility of the customer is [math]V(p,M) = v(p) + M - cn\,[/math]

A on the derivation of demand
Recall that [math]M=e(p,u)\,[/math], so that [math]v(e(p,u),p)=u\,[/math] when the expenditure function is evaluated at [math]p\,[/math] and [math]u\,[/math].
[math]d/dp(v(M,p)) = dv(M,p)/dm \cdot dM/dp + dv/dp = 0, where dM/dp = de(p,u)/dp\,[/math].
[math]\therefore q(m,p) = de(p,u)/dp = -frac{dv/dp}{dv(M,p)/dm}\,[/math]
[math]\therefore q(m,p) = -d/dp(v(p))\,[/math]

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