Problem Set 02-2018 PDF

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Contract Theory: Problem Set 2 14 April 2018 Complete the following assignments in teams of up to two students and hand in your solutions in class on 20 May, 2018.

Exercise 1 (Screening). A monopolist faces a customer who is one of two possible types, with equal probability, described by the utility functions: Ui (x, T ) : =

Z x

Pi (y)dy − T, i ∈ {1, 2}

0

P1 (x) : = 1 − x,

P2 (x) = 2 − x.

The monopolist’s cost function is C(x) = 0. The customer’s reservation utility is 0. 1. The monopolist offers his customer a menu of price-quantity combinations: M := {(x1 , T1 ), (x2 , T2 )}, from which the customer is free to choose one (and only once). What are the optimal price-quantity combinations? ¯ := {(t1 , f1 ), (t2 , f2 )}, 2. Suppose the monopolist offers instead a menu of two-part tariffs, M where fi is a lump-sum fixed fee and ti the price charged per unit. What are the optimal two-part tariff? ¯ more profitable than M for the monopolist? 3. Compare your results from [1] and [2]. Is M Why (not)?

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