Imagine a monopoly with 100 consumers. Consumers may be of two types according to the following demand functions: p1 = 8 2q1 and p2 = 2 - q2. The marginal cost of the monopolist is constant and equal to 1 Euro. There are no fixed costs. The percentage of consumers of each type is 50%.

a) Compute the optimal two-part tariffs for the monopolist if it is capable of perfectly discriminate between the two types of consumers (first degree price discrimination).

b) Suppose the Government decides to ban this type of discrimination and forces the monopolist to set a uniform price equal to both consumers. What is the optimal uniform price for the monopoly? (Note: The Government does not care if the price is low or high)