Struggling with this one
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.
(a) Consider an employer deciding whether to hire a new employee who will produce a marginal value product of MP. If the employer offers income and no health insurance, what wage, w, will the employer have to pay the employee in a competitive labor market? What would happen if the employer offered the employee less? What would happen if the employer offered the employee more?
(b) D is a measure of job-specific human capital; as workers learn the job, they become more productive so D > 0. However, not every job or industry has the same value for D. In some lines of work D is low, while in others D is high, simply because of the nature of the work. Given the results you have seen in this problem, in which types of industries – high-D or low-D – would you expect there to be a larger fraction of employers offering pooled health insurance to workers?