Topic 4: Adverse Selection, Signaling and Screening

Transcription

1 Rachel Kranton, Department of Economics, University of Maryland: ECON 604 Spring 2001 Lecture Notes Topic 4: Adverse Selection, Signaling and Screening ² Uninformed Sellers and Adverse Selection Basic Set-Up Productivity is Observable Productivity is Private Information ² Signaling: Spence ± Situation 1: Focus on Costs of Signaling Separating Equilibria Pooling Equilibria Multiple Equilibria, Re nements, and the Intuitive Criterion ± Situation 2: Costs and Bene ts of Signaling ² Screening First-Best (Types are Public Information) Subgame Perfect Equilibria Screening by a Monopolist

2 The Issue Asymmetric information (hidden information) Examples: (i) a worker has more information about own ability than a potential employer (ii) an individual has better information about own health status than a potential insurer (iii) a seller of a product has more information about the quality of the product than a potential buyer (iv) a buyer of a product has greater information on how much she values the product than does the product s seller. First-Best Outcome versus Equilibrium Market Outcome: with hidden information the market outcome will generally be ine cient (adverse selectionproblem). Research on institutions or mechanisms to improve on the market outcome: signaling and screening. 2

3 Uninformed Buyers and Adverse Selection Basic Setup: There are many employers/ rms. they have CRTS technology and are risk neutral. the price of output=1.. There are many workers, normalized to measure 1. workers di er in ability/productivity: µ»f( ) on [µ,µ] ½R. f(µ) is the contribution to a rm of a worker with abilityµ r(µ) is the opportunity cost of a worker of typeµ of accepting employment in one of these rms. 3

4 First best outcome:µ is observable Letf(µ) =µ: Perfectly competitive rms each will hire labor up to the point were MRP=MC, or µ =w. The equilibrium wage for a worker withproductivityµ is then: w (µ) =µ: The only workers who are willing to work for that wage are those for whom r(µ) w (µ) =µ. Pro ts to a rm from employing a worker of productivityµ are: µ w Workers withproductivity µ 2 [r(µ);µ] are employed. This is the Pareto optimal outcome: 4

5 Productivity is Private Information w cannot depend on any individualµ of a worker. Insteadw will depend on the distribution of productivity conditional on a worker accepting to work: The set of types of workers who accept to workat wage ratew (the labor supply) is: (w) = fµ jr(µ) wg The average productivity of those workers who will work at wagew(the labor demand) is: w solves: or E [µ jµ 2 (w)] E[µ jµ2 (w )] =w : E[µ jr(µ) w ] =w : The equilibrium is characterized by a xed point. Typically this equilibrium will not be Pareto Optimal. 5

6 Productivity is Private Information (cont.) Special case:r(µ) r,wherer 2 (µ,µ). Pareto optimality: all workers withµ 2 [r;µ] should be employed. The labor demand is then:e[µ jµ 2 (w)] =E(µ). In equilibrium, we havew =E(µ) and (w ) = [µ;µ] forw r = ; forw <r: 6

7 Productivity is Private Information (cont.) The type of equilibrium depends on the relative proportions of high and lowµworkers. If there are many low productivity workers, w =E(µ)<r, and no workers are hired. If there are many high productivity workers, w =E(µ) r, then all workers are hired. Relative to the Pareto-optimal level, too few workers are hired in the rst case and to many in the second. 7

8 Productivity is Private Information (cont.) General case:r(µ) strictly increasing inµ. Assumer(µ)<µ for allµ. The equilibrium wage will be: E[µ jr(µ) w ] =w : To determine the equilibrium outcome, nd the xed point. De neá(w) =E[µ jr(µ) w]. Forw =r(µ);á(w) =µ Forw r(µ);á(w) =µ;á(w) =E(µ) 8

9 Productivity is Private Information (cont.) The equilibrium is ine cient: high productivity workers are not employed. Observe thate(µ)>e[µ jr(µ) w ]. This ine ciency could be very severe: Suppose thatr(µ) µ andr(µ) =µ. Also assume thatr(µ) is increasing and concave. Then essentially no workers are hired. 9