Compensation under profit maximization

Consider a profit-maximizing firm (with non-negative profits) that offers its employees compensation in the form of an annual salary ($50,000) and health insurance (annual $15,000 premium). The annual, per employee compensation cost is therefore $65,000. (I’m ignoring all taxes.)

Now imagine a law is passed that outlaws employee-sponsored health insurance. Maybe health insurance is provided in a Medicare-for-all type program or some other way. That’s not important. What’s important is now the firm does not offer the $15,000 premium coverage. But, it still may offer a salary. Assume nothing else changes.

If the firm is still profit maximizing, what salary does it offer under the new law?

(A) $0

(B) $50,000

(C) $65,000

(D) 6 chickens

Think it over before reading the answer below.

Since the firm was profit maximizing before the law, it means that the total, per employee compensation of $65,000 was optimal (with respect to profits). Had it offered more — either higher salary or more in health insurance premiums — it’d have reduced its profits by overpaying for labor. Had it offered less, it also would have reduced its profits. This is by definition that it was profit maximizing at $65,000 total compensation (i.e., this is the unique value of compensation that maximizes profit).

But how would it have lost profit by paying less? One way is that it would not have retained the same personnel it was able to hire at $65,000. At lower compensation it would have only been able to hire less productive workers. The workers it could have had at $65,000 would have gone to another firm that offered a better deal or they could have taken more leisure. The story doesn’t really matter. The point is that the profit maximization assumption is doing some work. It is pinning down the cost of labor at its optimum. It is telling us the price at which labor market supply and demand meet.

If the firm is still to maximize profit after the law is passed, it certainly cannot offer more than $65,000. If it required more than $65,000 in compensation to retain the profit-maximizing labor force after the law passed, then it would have required more than that sum before hand. Remember, nothing else changed except the outlawing of compensation in the form of health insurance. On the other hand, if it maximized profit to provide less than $65,000 in compensation after the law passed, then the firm was not profit maximizing before hand. If its (presumed profit maximizing) labor force were willing to work for less, then it’d have accepted a lower salary before hand. But that violates the assumption that the firm was profit maximizing before passage of the law.

An alternative argument is that if the firm doesn’t offer at least $65,000 in compensation, some other firm will set up shop next door with identical structure. This new firm will compete for labor and the competition will bring the market rate of compensation back up to $65,000. (We assumed a firm of this type can afford $65,000 in compensation and still make a profit. That’s what occurred before the law passed.)

(A) and (D) are clearly wrong. I bet some readers were tempted to choose (B), figuring that workers were satisfied with $50,000 in salary before, so should be afterwards. But if that was all a worker wanted from the job, then the employer shouldn’t have offered to pay for health insurance. In other words, (B) violates profit maximization. The worker was not satisfied with just $50,000 in salary. She demanded another $15,000, taken in the form of a health insurance policy, and the employer obviously found it optimal to provide it.

By now you know that (C) is the correct answer. Now, this was all fairly theoretical. But it has real-world applications. I’ll leave it as an exercise for the reader to apply it to this post by Sarah Kliff. Note that many empirical studies support the idea that when employer-paid health insurance premiums go up (down) wages go down (up) by the same amount. Now you know why.

@afrakt

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