lecture4 - Econ 103C-Lecture 4 Adverse Selection David...

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Econ 103C-Lecture 4 Adverse Selection David Sraer U.C. Berkeley February 25, 2008 David Sraer (U.C. Berkeley) Econ 103C-Lecture 4 February 25, 2008 1 / 49
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A refresher on adverse selection Adverse selection refers to situation where one party to a transaction owns, before the contract is signed, some private information about a characteristics involved in the transaction. Examples abound: a car dealer and the car quality; a buyer of the good and his valuation for the good; an entrepreneur and the profitability of its project. Contractual design can help overcome the risk of no-trade that these information asymmetries inflict. David Sraer (U.C. Berkeley) Econ 103C-Lecture 4 February 25, 2008 2 / 49
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The simple economics of adverse selection We begin with a very simple model of buyer discrimination due to Mussa and Rosen (1978) The situation is one where a seller wants to sell a certain number of the same good to a buyer. The seller ignores the buyer’s valuation of the good, i.e. how much the buyer is willing to pay for a quantity q of the good. Assume the buyer’s utility is represented by: U ( q , T , θ ) = θν ( q ) - T q is the number of goods purchased by the buyer. T is the amount paid to the seller. θ is the type of the buyer: a higher type enjoys a higher utility from consumption for any given level of consumption. ν ( q ) is the utility derived from the consumption of q units of the good for a type θ = 1. We assume ν is C 2 , strictly increasing and strictly concave with ν (0) = 0. David Sraer (U.C. Berkeley) Econ 103C-Lecture 4 February 25, 2008 3 / 49
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The simple economics of adverse selection (2) The type θ is private information to the buyer, who only knows the a priori distribution of θ in the population, i.e. θ F () The seller’s profit is: π = T - cq , where c > 0 is the unit production cost of the good. Question: What is the optimal pair ( T , q ) that maximizes seller’s profit? (we assume the seller offers the contract) To simplify matters, assume there is just two types in the population of buyers, i.e. θ = θ L with probability β or θ = θ H > θ L with probability 1 - β David Sraer (U.C. Berkeley) Econ 103C-Lecture 4 February 25, 2008 4 / 49
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First Best Outcome As we did in the moral hazard case, we take as a benchmark the case where the buyer’s type if observed and verifiable by the seller. In that case, a contract specify a pair ( T i , q i ) for each of the type i ∈ { L , H } . The only constraint to the seller is that the buyer wants to buy the good, i.e. that he derives a utility greater to what she could achieve by refusing the contract. Let u be this outside option’s utility and assume it is exogenous. = This is an (IR) constraint: θ i ν ( q i ) - T i u Thus the seller’s first best program: max ( T i , q i ) T i - cq i θ i ν ( q i ) - T i u David Sraer (U.C. Berkeley) Econ 103C-Lecture 4 February 25, 2008 5 / 49
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Two part Tariff as first best contract Linear programming with convex constraint = we can apply Kuhn-Tucker necessary conditions.
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