A monopolist produces a good with constant marginal cost equal to c, c < 1. Assume for now that all consumers have the demand Q (p) = 1 - p. The population is of size 1.

1. Suppose that the monopolist cannot discriminate in any way among the consumers and has to charge a uniform price, p^U. Calculate both the price that maximizes profits and the profits that correspond to this price.

2. Suppose now that the monopolist can charge a two-part tariff (m, p) where m is the fixed fee and p is the price per unit. Expenditure then is m + pq. Calculate the two-part tariff that maximizes profits and the profits that correspond to this tariff. Compare p^U and p and comment briefly. Compare the situation with a uniform price and a two-part tariff in terms of welfare (a verbal argument is sufficient).

3. Assume now instead that there are two types of consumers. The consumers of type 1 have the demand Q₁(p) = 1 - p, and the consumers of type 2 have the demand Q₂ (p) = 1 – p/2. The population is of size 1 and there are equally many consumers of the two types. Finally, it is assumed in this question that c = 1/2. Calculate the two-part tariff that maximizes the profits of the monopolist. Compare the two-part tariffs found in questions (2) and (3) for c = 1=2 and comment briefly.