Difference between revisions of "Baye Morgan Scholten (2006) - Information Search and Price Dispersion"
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==Search Theoretic Models of Price Dispersion== | ==Search Theoretic Models of Price Dispersion== | ||
− | The general framework used through-out is as follows: | + | The ''general framework'' used through-out is as follows: |
*A continuum of price-setting firms with unit measure compete selling an homogenous product | *A continuum of price-setting firms with unit measure compete selling an homogenous product | ||
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*The indirect utility of consumers is: | *The indirect utility of consumers is: | ||
<center><math>V(p,M) = v(p) + M\,</math></center> | <center><math>V(p,M) = v(p) + M\,</math></center> | ||
− | where <math>v(\cdot)\,</math> in nonincreasing in <math>p\,</math>, and <math>M\,</math> is income. | + | <center>where <math>v(\cdot)\,</math> in nonincreasing in <math>p\,</math>, and <math>M\,</math> is income.</center> |
*By [http://en.wikipedia.org/wiki/Roy%27s_identity Roy's identity]: | *By [http://en.wikipedia.org/wiki/Roy%27s_identity Roy's identity]: | ||
<center><math>q(p) \equiv -v'(p)\,</math>.</center> | <center><math>q(p) \equiv -v'(p)\,</math>.</center> | ||
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<math>\frac{dM}{dp} = \frac{de(p,u)}{dp}\,</math>. | <math>\frac{dM}{dp} = \frac{de(p,u)}{dp}\,</math>. | ||
− | <math>\therefore q(m,p) = \frac{de(p,u)}{dp} = -\frac{dv | + | <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>\\ | <math>\therefore q(m,p) = -\frac{d}{dp(v(p))}\,</math>\\ |
Revision as of 20:38, 25 January 2010
- 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:
- The indirect utility of consumers is:
- 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
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].
[math]\frac{d}{dp(v(M,p))} = \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]\\
[math][/math] [math][/math] [math][/math] [math][/math]