## INFORMATION PROVISION: Equilibrium with Perfect Information

Posted by Kathryn Schwartz on July 13, 2014
INFORMATION PROVISION

Next consider the situation where consumers costlessly observe the price and quality of the product offered by each firm prior to making their purchases. Given the firms’ price-quality combinations ( As before, to solve for the Nash equilibrium in prices, we derive market shares for each firm. The marginal consumer who is indifferent between qH at price pH and qL at price pL is given P by: 0 = -2L_L = A . Similarly, the marginal consumer who is indifferent between purchasing qL and making no purchase has a valuation of: 6 = — . Thus, the market share for the high quality firm is 1 – A
Each firm chooses price to maximize profits, which are found by multiplying price-cost margins by market share. Equilibrium prices are given by:

Prices are increasing in both own and rival’s marginal costs. Prices also increase as quality differentiation increases. If there is no quality differentiation, qH = qL, = p^ = с , and profits for each firm equal zero. If we were to allow firms to choose quality levels in the first stage of a two stage game, firms would choose to differentiate themselves from each other in order to soften subsequent price competition. In markets with quality differentiation, both firms will earn positive profits at least large enough to cover fixed costs. Under our model, market forces will lead to product differentiation. This replicates an important aspect of the child care market.

Comparison

We now turn to a comparison of equilibrium prices with imperfect information and those with full information. Following the literature, we focus attention on three characteristics of the price distribution: price dispersion, maximum price, and average price. Because our model contains two firms, price dispersion is measured as the difference between the high and the low price. Change in price dispersion due to search is given by:

Thus, the following proposition is immediate:

Proposition 1 If xH~2. xL, markets with imperfect information will have more price dispersion.

For xH 2; xL, consumers who do not value quality highly must have a lower or equal willingness (i.e. higher or equal search costs) to continue searching than consumers with higher valuations for quality. To put it somewhat differently, consumers who value quality highly are weakly more inclined to keep searching until they obtain a good match than are consumers who have lower valuations for quality. Alternatively, lower valuation consumers must be more inclined to either drop out of the market or stay at the first provider they encounter.