The following question considers the possibility that employer provided health insurance
The following question considers the possibility that employer-provided health insurance reduces job mobility—a phenomenon that has been termed job lock. Job lock prevents workers from transitioning to jobs in which their marginal productivity would be higher than at their current jobs. Consider three workers with the following preferences:
Uij = Wij+ (50 × Hij)
Ukj = Wkj + (110 × Hkj)
Ulj = Wlj + (150 × Hlj)Ulj
where Wij is the wage at job j for worker i, Hij is an indicator variable (i.e., it takes on a value of one or zero) for whether or not employer-provided health insurance (EPHI) is offered to worker i at job j. Assume that there are no employee copayments for the insurance and that the labor market is perfectly competitive. Workers i, k, and l all have a marginal product of $200. There is an arbitrarily large number of firms in the economy, and they cannot offer worker-specific compensation packages. If they provide EPHI to one worker, they must provide it for all their workers. EPHI costs firms $100per worker. Assume that there is full employment—all three workers will be employed.
a. What wage does each of these workers earn? Do they have EPHI? What is the compensating wage differential for EPHI (the labor-market-wide decrease in wages at a job that provides EPHI)?
b. Now assume that there are two types of firms: type 1 and 2. Type 1’s cost of providing EPHI is $200 per worker and type 2’s cost of providing EPHI is $100. At which type of firm is each of the three workers employed? Why? Which workers have EPHI?
c. Now assume that firms of type 1 develop a new technology that increases the marginal productivity of their workers to $230. At what firms do the workers work now? Are any of them suffering job lock?
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