Baye Morgan Scholten (2006) - Information Search and Price Dispersion
- This page is part of a series under PHDBA279B
Key Reference(s)
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:
- 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(M,p)}{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(M,p)}{dp}}{\frac{dv(M,p)}{dm}}\,[/math]
[math]\therefore q(m,p) = -\frac{d}{dp(v(p))}\,[/math] in our case.
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