• 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.


    • In the long view, if one sees a new normal where costs to firms drop due to a market reset (majority of firms begin to transfer HC expense to feds), and profit maximization curve shifts, the conventional wisdom–theme of SK’s post–may evolve, no?

      Most of what I read on this subject (granted, its all prognostication) mistakes anticipated future behavior with the reality of what is in place now. Big difference, and that is the error.


    • One other factor to consider in the current market: sticky wages. People *really* don’t like their pay to go down. In a theoretical system, as demand drops salaries would also decline. However, what we actually see is that salaries don’t increase, but they don’t drop. People get fired and take a new job for a lower salary, but the current salary at the current job is *very* sticky. Dropping health insurance would be an “acceptable” way to have a $16,000 pay cut without loosing too many of the current employees. Even if it turned into a smaller subsidy (say $8000) the company would still be ahead.

      This assumes we’re still at a high unemployment situation.

    • Interesting post. GIven the extreme inefficiency of the health care system, it would also mean that a dollar of wage lost to premiums is more than a dollar loss in total utility to the worker.

      • The tax advantage of health insurance premiums causes the distortion.

        • Apart from taxes, there are also the distortions caused by adverse selection in the individual market. If employer health insurance were outlawed, the employer would have to pay the employee more than $65k to retain him/her because group insurance (especially large group insurance) is less expensive than individual insurance. To get the same benefits, the employee would have to pay more in the individual market because of the adverse selection distortion.

          • That presumes the alternative is the individual market as we know it. There are other alternatives, one of which I mentioned in the post. In any case, it isn’t correct to reason what the employer must do from the basis of what it would cost the employee to obtain other coverage. The employer will do whatever is necessary to maximize profit. What that is depends on what the employers’ competitors do. There may be an equilibrium that does not require super-$65k compensation, even if the workers’ health care costs rise. One can imagine that the employer (and all its competitors) cannot stay in business if they offer higher compensation. In that case, the law is an effective compensation cut. Stranger things have happened!

    • I accept the basic premise. However, I’ve heard a number of union folks dispute it. They simply don’t feel that employers would give them the money back, probably based on experiences bargaining with them.

      Of course, in their negotiations, unions have faced the tradeoffs between wages and health benefits, and they have generally gone for greater health benefits. So, their assertions are a bit contradictory to their own experience. And certainly they had a bit of a vested interest in opposing any change to the taxation of health benefits.

      But back to Austin’s point – are there circumstances where workers would not see all of their total compensation returned to them? Like large disparities in bargaining power between management and labor, like in low wage non-unionized jobs? I’m not a labor economist, so I don’t know. Like I said, I accept the general principle. But if the scenario above actually materialized, I would not be surprised if workers didn’t see the gains – after all, workers have generally not seen the gains from their increased productivity since about the 60s or 70s. Capital has seen all those gains.

      • One has to be very clear about the counterfactual. You usually cannot measure the premium-wage trade-off with a simple pre-post analysis. Too much else changes. (That’s why I emphasized in the theoretical set up to the post that nothing else changes.) The point is that when premiums go down (up), wages go up (down) to in the same amount, relative to what they would have otherwise been. We don’t know what they would have otherwise been unless we have a very clever empirical design. See the papers in the posts I linked to.

        Just to drive the point home, if premiums go down and wages go down, that doesn’t mean wages aren’t higher by the reduction in premiums relative to what they would have otherwise been. Theoretical and empirical work has shown they are precisely that, though of course there is a lag and it is an average effect. Nothing is instantaneous and homogeneous in the real world.

      • “are there circumstances where workers would not see all of their total compensation returned to them?”

        Those circumstances are called real world experience.

        • Just look for instances where my explicit (profit maximization) or implicit (only two types of compensation) assumptions don’t hold. For sure, not all organizations are profit maximizing at all times. Absolutely, health care and wages are not the only forms of compensation. There may be other examples.

          • I’m not an economist but, for me, “profit maximization” implies perfect information. The employer knows at what point any given employee will choose to take their talents elsewhere and has discovered the compensation point of perfect equilibrium, not so high that they’re overpaying, not so low that the employee is tempted or compelled to leave. That doesn’t sound like any employer I’ve ever known and the point of equilibrium would differ from employee to employee even were the employer able to reach perfection for one employee. (It also assumes that employees have unique talents which are hard to find rather than simply being relatively interchangeable parts that an employer can easily replace. The first of which is also, from my limited experience, not much of a real world situation for the majority of employees.)

            Here’s how I think it would play out in the real world. Most people get a paycheck and see their cash compensation and how much is deducted for their share of a health insurance premium. The vast majority are vaguely aware that their employer pays some percentage of the total cost of the premium, but the employee really isn’t clear on what that exact amount is.

            Using your example, an employee receives $50,000 cash compensation (ignoring taxes) and sees an annual deduction of $3,000 for their 20% share of the premium cost. If the employer simply stops paying their share and tells the employee to go find insurance on the individual market, the employer says we’ll continue to “give” you an amount to cover your costs at finding insurance, a very generous $6,000, twice as much as you’ve been paying out of pocket for your insurance. The employee now has $9,000 ($3,000 + $6,000) and appears to receive cash compensation of $56,000 compared to his compensation of $50,000 the year before. Big win! The employer is actually $6,000 a year ahead on the employee, which most employees won’t know but their employer certainly will know it.

            I think most people have an instinctual understanding of this: if the employer stops providing health insurance, the employee will not gain but the employer will. It might not fit a model of “profit maximization” but this feels more like the world employees experience. And when labor is plentiful and unemployment high? The employee is going to really catch the short end.

            • It’s fine to speculate and theorize. That’s what I was doing as well. Only, I did one more thing, which is point to empirical studies (well, to posts that point to studies). The premium-wage trade-off is well established. No reason you have to believe it!

              Also, be sure to read all the comments, in particular the ones about the proper counterfactual and that in the real world this won’t happen overnight. Given that, your story may be correct in the short-term, and mine in the long-term. Still, I take comfort in evidence, not merely in hypotheses.

            • “‘profit maximization’ implies perfect information”

              No. They are two different things. Perfectly competitive markets imply both. I’m actually on the fence as to whether my set-up requires competition at all, but if it does, I don’t think it need be perfect.

    • Austin dodges the scenario currently facing many American employees though: In an economy where unemployed workers outnumber job openings 4 or 5 to 1, if suddenly “someone else” (presumably government) takes the burden of providing health insurance off of everyone’s spreadsheet, why wouldn’t most or all of the current premium for private health insurance not be captured by the employer (i.e. the worker gets the same $50K in salary but no $15K bump up)?

      In such a scenario, most dissenting employees (unless they are in extremely obscure fields) know that they cannot leave the company in protest for it keeping all the health insurance premium. The company gets away with keeping the $15K. Now maybe economy-wide, every employee slacks off more due to lowered morale… but as long as it is systemic, no employer benefits by unilaterally increasing their pay to the prior “profit-maximizing” level… because industry-wide, all “profit-maximizing” levels have reset to $50K per worker as a result of the healthcare policy change by government.

      I can cite the example of my own employer, who has frozen wages since 2007, not hired a single new employee to replace natural leavers (i.e. retirees) and has shifted more and more of the cost-sharing for the healthplan to the employee… in net effect, massively decreasing wages. If the government suddenly passed single-payer, rendering our private healthplan redundant, I can easily foresee my employer keeping whatever it is that they pay them. And since I have no idea what they pay them, I don’t even know how much net compensation I’m losing… so even if I felt confident enough to ask for a raise (which I don’t in this economy), I don’t know what I “should be making” if Austin’s assertion is true and the employer should be indifferent to giving me what they would have given the insurance company.

      Thoughts, Austin?

      • If there are workers waiting in the wings, explain to me why a profit-maximizing employer facing competition in the labor market and from other firms offers insurance now? Your example of your own employer’s behavior is exactly what one would expect. Whatever compensation is required ex ante, the same is required ex post. I think you are blurring the two time periods. Also, in real life, these things take time to settle out. We may not have hit labor market equilibrium yet.

        • They offer health insurance now because they know that almost all other employers in my field of work offer health insurance. (My employer also offers paid transportation to/from work, in accordance with past practice of all other employers in my industry offering free transportation to/from work.) So you’re right in the basic assumption that I took my job based on its total compensation package, not just because of the nominal salary attached to it.

          But here’s the rub: there are components of my salary that I have no idea how to value. I have a very limited idea how much it would cost to buy a transportation service or healthcare coverage comparable to what I already have… and I have no idea what my actual employer has used its considerable size and power to negotiate (I assume it’s cheaper than buying it on my own). Thus my salary is roughly (using your example with modifications to my own circumstances):

          $50K in actual cash + $X in healthcare benefits + $Y in transportation benefits = $Z in all other benefits

          Since the employer knows exactly what X, Y and Z are (and I don’t), I’m at a distinct disadvantage. I don’t know if my total compensation is $65K or $80K or $100K. So what if all healthcare is taken over by someone else, and the employer comes back to me and says “Oh, well, here’s $60K and you’ll keep your other benefits” and pockets the other $5K? Or what if the employer says “Well, the cost of Y and Z are rising and that offset X, so your base salary stays at $50K”?

          You seem to be arguing that, in a world of complete and transparent salary information, the employer couldn’t game the system by withholding the $15K. But in practice, no employee knows whether they are being cheated by their employer – or grossly overpaid by their employer – relative to anyone else in the marketplace… but the employer does know this information. Therefore, I find it much more likely in the short-term that the employer will keep the $15K… at least until many years pass by and we reach full employment again so employees can feel safe to search for another job and discover that other employers did convert healthcare to wages at a ratio much more 1-to-1.

    • I will also give you a real-life example of why I believe employers will keep the health premium if given a mechanism to undo the historical accident (post-WWII wage controls) that led to them providing it in the first place:

      When employers used to provide pensions, they paid the lion’s share of their cost. Sure, employees paid some token % of their income towards it… but most of the cost was borne by employers. They hated this promise they made in good times when bad times finally arrived and switched to defined contribution schemes like 401k’s.

      Have you looked at whether every company kept their contributions the same as when they were maintaining pension plans? They should have, if what you say is true about the company being indifferent as to whether they pay the $65K in total comp as “wages,” “healthcare” or in this case “retirement funds.” But, as we see now post-2008, a lot of companies have simply dropped the pretext and are no longer matching 401k contributions at all. (Mine stopped.) Presumably, a lot of companies are simply keeping that portion of what used to be “employee compensation”… which leads me to believe that they’ll do the same with health insurance.

      Please look into what happened with pensions turned to defined-contributions turned to no-contributions… and see if it resembles what could happen to employer-sponsored health insurance.

      • This is not a coutnerexample. This is part of a trend I acknowledge. The labor supply and demand curves shift over time. This is why the appropriate counterfactual is important. Again, see the studies. Since we can’t seem to talk to each other, let’s stop talking past each other. This is my last response.

    • Isn’t there some redistribution effect present in the provision of health insurance that might skew how wages would actually fall out in your scenario? While employers do not have to offer coverage to everyone, they have to offer the same coverage to employees within a class. Absent this requirement, would Junior Mid-Level Manager still be expected to retain the $15K in wages, or would it be redistributed upwards to the Senior VP who “merits” $30K in health coverage (or wages)?

      • In the theoretical world and with the assumptions provided in the post, if the employer wants to retain the exact mix of labor it has, it can’t change anyone’s compensation. In the real world, things are not that precise, so I would expect this to be an average effect over broader classes of labor, not necessarily at the individual level.

    • You can refuse to answer this if you like, because I think I’m annoying you with my disagreement on how your initial scenario would play out (i.e. that as health care insurance costs for the company decrease, wages would increase by the same amount). I think that real-life experience bears out my predictions that B (not C) is closer to the correct answer to your original question… but I guess over time, we’ll see what happens when ACA takes full effect and employers experiment with dropping health cover.

      However, I want to know how you think family coverage and non-participation by employees plays a role in deciding whether a company can “get away with” keeping some or all of the hidden health insurance component of employee compensation. Two scenarios:

      (1) Employees Smith and Jones both are hired at the same time, with the same qualifications and experience for the exact same job. Both perform exactly the same. Both are hired at a time when they are single, but then Smith goes off and gets married and has a kid right away. Jones remains single. The company covers singles at $50 per payperiod deduction while families are covered at $100 per payperiod deduction. It costs the company $25K to cover a “family” versus a “single” person at $15K. Smith is effectively making more than Jones under this scenario for completing the same amount of work ($75K vs. $65K). The company hits tough times and dumps health cover. Do you predict that the company would increase Smith by $25K(-$1200 for eliminating the pay deductions) and Jones by $15K(-$600) to hold each one at exactly the same level of compensation that they were getting before? Or does Smith lose out here by resetting all wages to $65K? If someone loses out, then doesn’t that mean that companies can keep some of the compensation when benefits are translated strictly into wages… rendering the assumption that “when health insurance costs go down, wages go up by the same amount” false?

      (2) Same scenario as above, only Smith this time stays single and is a Young Invincible, foregoing health insurance completely because he wants the extra $50 in his paycheck. So now, when the company dumps health insurance completely, does he get to “free ride” on that decision, seeing his wages go up even though before he wasn’t getting paid $65K at all – he was strictly working at $50K? Or can the company point to him when talking to Jones and say, “he’s working for $50K, so should you” when they decide to not bump up Jones’s salary to compensate him for the health insurance they’ve taken out of his total compensation?

      I’m not trying to annoy you with these questions. They are a part of real-life… and as a regular reader of this blog, I almost always agree with your viewpoints… but this post really seems kind of naive, especially when you suggest that many people foolishly fall for answering your question with B instead of the perfectly-rational-and-still-sounds-wrong C. C sounds wrong especially in the short-term because it is not the experience many people encounter when dealing with real world employers who represent benefits as if they have no monetary value when dealing with the employee (“you can’t cash out the health care benefit – take it or leave it as-is”).

      • You’re not understanding me. That is all. I’m not even disagreeing with what you think we’d observe in the real world. I’m saying you’re not understanding what the proper counterfactual is. Recognize that we don’t get to observe the counterfactual world, so it takes a very special situation to measure the true effect. Studies have done that, but you refuse to acknowledge that fact. Do you think the studies are wrong? Please show me how and where. The set-up in this post assumes away a lot of the dust and smoke we normally observe in order to make the counterfactual clear. That’s why I wrote that nothing else changes. That does a lot of work. It means we can use pre-post to measure the effect of the policy. You cannot do that in the real world. But that’s what you keep arguing. Please try to understand this before posting again.

        Also, you keep ignoring what I’ve already explained in the comments, that in the real world, this effect takes time. It is a transition between states of equilibrium, not something that happens instantly. Can you acknowledge that?

        For these reasons, we won’t just “see what happens when the ACA takes full effect.” What you’ll naively see won’t be the effect I’m describing. It’ll be confounded by many other factors that need to be controlled for. (This is the “true counterfactual” problem again.) Someone may do a proper study, if they can figure out how to do it. We’ll have to wait for that. For the time being, go back to all the studies that have already been done.

        That I’ve written essentially the same thing several times without any sign of acknowledgement that you are trying to get it, I am annoyed. Sorry. If you aren’t understanding what I’ve written, just ask a question. Saying it just seems naive is insulting, considering I’m not just making this stuff up.

    • Hmm. Seems to me that it should matter if the Gov offers some sort of subsidy or “medicaid-for-all” arrangement. If the gov does nothing, then the worker clearly sees total compensation fall by 15k, all else equal.

      BUT if gov provides insurance worth 15k, with no change in wages, equivalent of total compensation remains at 65k.

      • You’re in the ball park b/c the HC that’s “provided” has to be paid for somehow, so the gov’t would need to get $15k from somewhere and likely that would be taxes, which likely would apply to the employer and the employer would likely count them as employment related and hence you’re back to $65k.