Difference between revisions of "Baye Morgan Scholten (2006) - Information Search and Price Dispersion"
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*A mass <math>\mu</math> is interested in purchasing the product | *A mass <math>\mu</math> is interested in purchasing the product | ||
*Consumers have quasi-linear utility: | *Consumers have quasi-linear utility: | ||
| − | + | <center><math>u(q) + y\,</math> where <math>y\,</math> is a numeraire good</center> | |
*The indirect utility of consumers is: | *The indirect utility of consumers is: | ||
| − | + | <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. | |
*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> | |
*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 | ||
| Line 26: | Line 26: | ||
'''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> | |
| − | + | <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>\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> | |
| + | </center> | ||
<math></math> | <math></math> | ||
Revision as of 20:30, 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 [math]V(p,M) = v(p) + M - cn\,[/math]
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, where 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]
