Q1. Consider the adverse selection model, where the ability of each worker, 0, can be 1, 2 or 5. Workers observe their own abilities, but firms only observe the overall distribution of probabilities (1/3, 1/6, 1/2). Suppose that the reservation value is r(0) = 0.5+0.50. (a) What is the range of wages, for which all workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker? Will there be a functioning labor market in this case? (b) What is the range of wages, for which no workers accept the competitive wage? (c) What is the range of wages, for which only lowest type workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker in this case? Will there be functioning labor market? 2140

Q1. Consider the adverse selection model, where the ability of each worker, 0, can be 1, 2 or 5. Workers observe their own abilities, but firms only observe the overall distribution of probabilities (1/3, 1/6, 1/2). Suppose that the reservation value is r(0) = 0.5+0.50. (a) What is the range of wages, for which all workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker? Will there be a functioning labor market in this case? (b) What is the range of wages, for which no workers accept the competitive wage? (c) What is the range of wages, for which only lowest type workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker in this case? Will there be functioning labor market? 2140

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.9P

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Consider a variant of the benchmark model of adverse selection. The types of workers (θ) are uniformly drawn from the unit interval [0,1]. A θ-type worker can produce θ units of some product if he is hired by firms. (Workers are the only input in the production.) The price of the product is normalised as 1. Before entering the labor market, workers decide whether to secure some certificate at a cost c ∈ (0, 1) or not. The certificate can fully reveal a worker’s type and he then decides whether to show it to firms or not. If a θ-type worker decides to quit the labor market, he can earn θ/4 from self-employment. Find the competitive equilibrium. (Hint, if a θ-type worker obtains the certificate and shows it to firms, he will receive a wage of θ from the market. For sure, he can also decide to join the labor market without obtaining or showing the certificate.)
A risk-neutral manager is attempting to hire a worker. All workers in the market are of identical quality but differ with respect to the wage at which they are willing to work. Suppose half of the workers in the labor market are willing to work for a salary of $40,000 and half will accept a salary of $38,000. The manager spends three hours interviewing a given worker and values this time at $300. The first worker the manager interviews says he will work only if paid $40,000. Should the firm manager make him an offer or interview another worker?
Question 18 Job-specific human capital In this problem, based on a simplified version of the model in Bhattacharya and Sood (2006), we will explore how linking employment and health insurance provision can (partially) solve the adverse selection problem if the labor market is competitive. Suppose that there are two types of workers – sickly workers with probability ps of falling ill over the course of the next year, and robust workers with probability pr < ps of falling ill. Employers cannot observe whether a worker is sickly or robust, and because of US law they can only decide to offer health insurance to all of their workers, or none at all. We will assume that a just-hired employee is less productive than an employee who has more experience; let MPn be the marginal value product of new employees, and MPe > MPn be the marginal value product of experienced employees. In this simple model, marginal value product depends only on experience, not on whether a worker is sickly or…
Job-specific human capital. In this problem, based on a simplified version of the model in Bhattacharya and Sood (2006), we will explore how linking employment and health insurance provision can (partially) solve the adverse selection problem if the labor market is competitive. Suppose that there are two types of workers – sickly workers with probability ps of falling ill over the course of the next year, and robust workers with probability pr < ps of falling ill. Employers cannot observe whether a worker is sickly or robust, and because of U.S. law they can only decide to offer health insurance to allof their workers, or none at all. We will assume that a just-hired employee is less productive than an employee who has more experience; let MPn be the marginal value product of new employees, and MPe > MPn be the marginal value product of experienced employees. In this simple model, marginal value product depends only on experience, not on whether a worker is sickly or robust.…
Suppose there are two types of people, high ability and low ability. A high-ability person's productivity is valued at wH = $100,000, while a low-ability person's productivity is valued at wL = $50,000. Assume that the employer does not know the ability of a job applicant, but knows that the probability of an applicant being high ability is 50%. Assume next that only high ability applicants can send a signal, i.e., obtain a degree. The employer pays the expected wage. i. What is the wage oer in a pooling equilibrium (no applicant attains a degree)? ii. What is the wage oer in a separating equilibrium (only high-ability applicants attain a degree)? iii. Suppose now both types can attain a degree, but it is costlier to attain for low-ability people and costs them cL = $60,000, while it costs high-ability people cH = $40,000. Is a separating equilibrium where only high-ability people send education as a signal possible? Explain.
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