3. There are two types of consumers for the product of a monopolist and there is 1 consumer of each type. The marginal cost of production is zero. The individual demand functions for a consumer of type i = {1,2} are given by: D1(p)=40-p D2(p)=40 - p/2 a) Suppose that the monopolist cannot tell the two groups and they intend to maximize their profit by the use of a single two-part tariff: T(q)=A+ pq. Calculate the optimal two-part tariff. b) Suppose that the monopolist cannot tell the two groups but now they intend to maximize their profit by the use of a menu of two separate two-part tariffs, T(qi)=A+ piqi, where i = {1,2}. Write down the four constraints that the monopolist faces when designing their menu of two-part tariffs. Explain the meaning of each constraint. c) Calculate the optimal menu of two-part tariffs. What are the prices, px, for each group? d) What are the fixed fees, Ai, for each group? e) Do either of the consumers receive an efficient bundle? Do either of the consumers have positive consumer surplus? Explain. 3. There are two types of consumers for the product of a monopolist and there is 1 consumer of each type. The marginal cost of production is zero. The individual demand functions for a consumer of type i = {1,2} are given by: D1(p)=40-p D2(p)=40 - p/2 a) Suppose that the monopolist cannot tell the two groups and they intend to maximize their profit by the use of a single two-part tariff: T(q)=A+ pq. Calculate the optimal two-part tariff. b) Suppose that the monopolist cannot tell the two groups but now they intend to maximize their profit by the use of a menu of two separate two-part tariffs, T(qi)=A+ piqi, where i = {1,2}. Write down the four constraints that the monopolist faces when designing their menu of two-part tariffs. Explain the meaning of each constraint. c) Calculate the optimal menu of two-part tariffs. What are the prices, px, for each group? d) What are the fixed fees, Ai, for each group? e) Do either of the consumers receive an efficient bundle? Do either of the consumers have positive consumer surplus? Explain