When xH 2: xu the high quality firm has a higher expected demand when information is imperfect than when there is full information. Under imperfect information, the high quality firm continues to serve all high valuation consumer in the interval [A, 1], as it did under perfect information. Now, this firm will also serve some lower valuation consumers, in the interval [AH, A], who happen to find the high quality firm first (see Figure 1). The low quality firm has a lower expected demand when information is imperfect.
As a result of lower expected demand, the low quality firm charges a lower price when information is costly to obtain than when it is freely available. Equation (7), which is unambiguously positive for xH > xL, shows that the high quality store either raises its price or does not lower by as much as the decrease in the low quality price. Consequently, we have the result that markets with imperfect information will have more disperse prices. Change in the maximum price due to search is given by:
After some algebra, we have the following proposition: f 3qh~2qA
Proposition 2 If xH > I – xL , imperfect information results in increased price dispersion and higher maximum price. [ ^h-Vl )
This result stems from the conflicting pressures on the high quality firm’s price. On the one hand, the high quality firm tends to charge a higher price because it faces higher expected demand under imperfect information than in a market with full information. On the other hand, it tends to charge a lower price as a strategic response to its rival, the low quality firm, which is charging a lower price due to lower expected demand. In order for the higher expected demand effect to dominate the strategic price response, high valuation consumers’ willingness to search must be sufficiently higher than the low valuation consumers’ willingness to search so that the high quality firm’s expected demand rises by enough to result in a price increase.
Change in the average price due to search is given by: