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 note 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].

Taking the derivitive with respect to [math]p\,[/math]:

[math]\frac{d(v(M,p))}{dp} = \frac{dv(M,p)}{dm} \cdot \frac{dM}{dp} + \frac{dv}{dp} = 0,\,[/math] where [math]\frac{dM}{dp} = \frac{de(p,u)}{dp}\,[/math].

[math]\therefore q(m,p) = \frac{de(p,u)}{dp} = -\frac{\frac{dv}{dp}}{\frac{dv(M,p)}{dm}}\,[/math]

[math]\therefore q(m,p) = -\frac{d}{dp(v(p))}\,[/math]\\

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