INFORMATION PROVISION: Equilibrium with Perfect Information 3

Posted by Kathryn Schwartz on July 17, 2014
INFORMATION PROVISION

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After some algebra, we have the following proposition:
Proposition 3 If xH >ь ’ imperfect information results in increased price dispersion, higher maximum price, and higher average price.

In order for search costs to raise average market price, the increase in the high quality firm’s price must be large enough to more than offset the decrease in the low quality firm’s price. The high quality firm’s price can only increase by enough if high valuation consumers are willing to search substantially more than lower valuation consumers. Indeed, high valuation consumers have be more than twice as willing to search as low valuation consumers in order for average prices to fall. It is straightforward to prove that if the condition for Proposition 3 is satisfied, so are the conditions for Propositions 1 and 2.

To summarize, we have shown that the need for costly search affects equilibrium price distributions in vertically differentiated markets. With relatively few restrictions, we are able to show that prices will vary less when there is full information. Obtaining the result that maximum prices and average prices decrease with information requires stronger assumptions on the relative willingness to search of low and high valuation consumers. To be specific, willingness to search must be positively correlated with the valuation for quality in order for the maximum price and the average price to decrease with information provision. In the remainder of this paper, we use this theoretical framework to help interpret our empirical results.
For each center, the data include information on center location, center affiliation, profit status and other center-level data The data also contain information on ages of children, prices and staff-child ratios at the group level for each group at each center. Such group-level or classroom-level data is rarely available for analysis.

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