The objective is to assess the incentive to acquire information on consumer characteristics. We consider a monopoly. The firm incurs no production cost. There are M consumers with unit demand. Consumers' valuation for that good, denoted v, is uniformly distributed on the interval [0, 1] . A consumer with a valuation v buys the good if and only if the price for the good p is lower than v (p ≤ v). The firm a priori does not observe the valuation v. Nevertheless the monopoly has the possibility to acquire information, which will lead to a partition of the consumers into N subintervals of equal length. For instance if N = 2, the monopoly knows whether a consumer has a valuation in the interval [0,1/2] or [1/2,/1] and can set two different prices for each sub-group.

1. Determine the optimal price for each sub-group.

2. Deduce the profit of the monopoly. Is there a benefit to invest in information acquisition for the monopoly?