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 clearinghouse that exhibit price dispersion. The survey is undertaken through two specializable frameworks, one for search and one for cleaninghouses, 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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