ECN611 Handout6

ECN611 Handout6 - Ec o no m ic s 6 1 1 H and o ut # 6 T HE...

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Unformatted text preview: Ec o no m ic s 6 1 1 H and o ut # 6 T HE E C ONOMIC S OF A SY MMET RIC INF ORMAT ION Chap. 13: Asymmetric info at the time of contracting: Adverse Selection and Screening Model I. [First just an equilibrium model without any game-theory flavor]: Competitive Output market; p = 1; w = p￿MPP = 1￿è Two kinds of workers: low and high productivity: èL < èH; Numbers: NL, NH; NL + NH = N Opportunity cost of employment: rL, rH Two cases: I. èi ' s are observable: At equilibrium, wL = èL; wH = èH. II. Workers know own èi; èi ' s are unobservable by firms. [So single wage, w.] Supply: Ni of èi offer to work if w ￿ ri [tie issue] È(w) = { è : w ￿ r(è)} Demand: Let ì = expected average productivity of those who accept employment. [This is ASSUMED to be ¯ if È(w) is empty.] è Definition (Akerlof): (w*, È*) is a competitive equilibrium if (i) È* = È(w*); (ii) w* = E(è : è ￿ È*) 611.06 - 1 A. It is possible that such an equilibrium is NOT Pareto optimal. Example: èL < rL = rH < èH [r = rL = rH] Then at any Akerlof equilibrium, Either way, E(è : è ￿ È*) = ¯; so at equilibrium, ¯ = w*. è è There must be unrealized contracts: Case 1. ¯ > r. Then w* > r and everyone works. Note: w* – r < w* – èL A firm would like to è offer a w￿ between these: w* – r < w￿ < w* – èL to a Type-L to quit since then w* – w￿ > èL. The Type-L would like to take this offer since r + w￿ > w*. Case 2. ¯ ￿ r. Then w* ￿ r and no one works. A firm would like to offer a w￿, r < w￿ < èH, to è a Type-H to work and a Type-H would like to take this offer. B. It is possible there is no equilibrium: Adverse selection and market unraveling: r(è) varies with è. Here: rH > rL. NL = 100 = NH; èL = 1/3; rL = 3/7; rH = 4/7; èH = 2/3. Note: èL < rL < rH < èH (1) Suppose È* = {èL, èH} E(è : è ￿ È*)) = [100￿(1/3)+100￿(2/3)] / [100+100] = ½ If w = 1/2, w > rL but w < rH; so È(w) = {èL}and only Type-L workers accept employment. (2) Suppose È* = {èL} then E(è : è ￿ È(w)) = èL = 1/3 < 3/7 and È(w) = ￿; Type-L workers also refuse employment. There does not exist an Akerlof equilibrium. That requires also looking at (3) È* = {èH} and (4) È* = ￿. 611.06 - 2 Model II. [now with game theory flavor] 611.06 - 3 Continuous case: Common knowledge: è distributed uniformly on [1, 2]; r(è) = .9è So, for example, E( è / r(è) ￿ 1) = E( è / 1 ￿ è ￿ 1.111...) = 1.05555... and E( è / r(è) ￿ 1.8) = E( è / 1 ￿ è ￿ 2) = 1.5. E( è / r(è) ￿ w) = ½ (1 + w/.9) for .9 ￿ w ￿ 1.8 An Akerlof equilibrium is found at w* = 1.125 and È* = { è / 1 ￿ è ￿ 1.25} We want to show this results from a pure subgame perfect Nash equilibrium. The SPNE strategies are: (i) For workers: A worker of type è accepts employment only at one of the highest wage firms and does so if and only if r(è) ￿ w* where w* is the highest wage offered. (ii) Both firms offer wage of 1.125 611.06 - 4 Clearly if r(è) > 1.125, switching to accepting employment at 1.125 makes the worker worse off. If r(è) ￿ 1.125, a worker can not be made better off by switching to not accepting work, or by switching to working at a lower wage firm. Notice that since E( è / r(è) ￿ 1.125) = 1.125, the firms are both earning a profit of 0. If a firm switches to offer less than 1.125, they get no workers, and get a profit of 0, no better than before. If a firm switches to offer w' > 1.125, they get all the workers and profit per worker is E( è / r(è) ￿ w') – w' < 0, worse than before. Q: For whom are there unrealized contracts? Exercises: 13B2, 13B5 611.06 - 5 ...
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This note was uploaded on 01/13/2012 for the course ECN 611 taught by Professor Kelly,j during the Fall '08 term at Syracuse.

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