Exercise 4: Price discrimination (1st degree) Consider the market of some good with a unique firm in it. In this market there are only two consumers, one of low valuation and one with high valuation. The firm is able to perfectly distinguish between them. Each consumer's gross consumer surplus is given by the following expression: U(0,4) = 0 ( 141 ) for i=1,2. The monopolist's cost function is given by C(q) = 244 +10, for i = 1,2. a) (3 points) Suppose the monopolist wishes to supply the market using packages. Set up the firm's maxi- mization problem, detailing the objective function and the constraints b) (3 points) Briefly explain why, at a solution, both constraints must hold with equality c) (3 points) Assume a = 2,61 = 10 and 62 = 15. Solve for the firm's optimal packages: (T1,91) and (T3,9) d) (3 points) Find the firm's profit under this solution e) (3 point) What is the market's total surplus? (Hint: you do not need to do any calculation to answer this question) Exercise 4: Price discrimination (1st degree) Consider the market of some good with a unique firm in it. In this market there are only two consumers, one of low valuation and one with high valuation. The firm is able to perfectly distinguish between them. Each consumer's gross consumer surplus is given by the following expression: U(0,4) = 0 ( 141 ) for i=1,2. The monopolist's cost function is given by C(q) = 244 +10, for i = 1,2. a) (3 points) Suppose the monopolist wishes to supply the market using packages. Set up the firm's maxi- mization problem, detailing the objective function and the constraints b) (3 points) Briefly explain why, at a solution, both constraints must hold with equality c) (3 points) Assume a = 2,61 = 10 and 62 = 15. Solve for the firm's optimal packages: (T1,91) and (T3,9) d) (3 points) Find the firm's profit under this solution e) (3 point) What is the market's total surplus? (Hint: you do not need to do any calculation to answer this question)