Difference between revisions of "Baye Morgan Scholten (2006) - Information Search and Price Dispersion"
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*There is a search cost <math>c\,</math> per price quote | *There is a search cost <math>c\,</math> per price quote | ||
*The customer purchases after <math>n\,</math> price quotes | *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> | + | *The final indirect utility of the customer is |
+ | <center><math>V(p,M) = v(p) + M - cn\,</math></center> | ||
'''A on the derivation of demand''' | '''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>. | 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>. | ||
<center> | <center> | ||
− | <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>d/dp(v(M,p)) = dv(M,p)/dm \cdot dM/dp + dv/dp = 0,\,</math>\\ where <math>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) = de(p,u)/dp = -frac{dv/dp}{dv(M,p)/dm}\,</math>\\ |
− | <math>\therefore q(m,p) = -d/dp(v(p))\,</math> | + | <math>\therefore q(m,p) = -d/dp(v(p))\,</math>\\ |
</center> | </center> | ||
Revision as of 20:31, 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:
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
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,\,[/math]\\ where [math]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]\\
[math][/math] [math][/math] [math][/math] [math][/math]