Three commenters whom I respect and whose work I respect–John Goodman, Tim Worstall, and Scott Sumner–made critical comments on my most recent blog post, “Fringe Benefits and Stagnating Wages.” My basic point is right, but I blew the equilibrium.

I realized this when wondering why both John Goodman and Scott Sumner thought I had left out the tax on employers of 6.2% for Social Security and 1.45% for Medicare. Of course, I mentioned the tax, but told readers they could skip that paragraph. That was wrong.

Not only did I blow it on the margin, but also I blew it on the infra margin. Let me explain.

When the government taxes pay in money, it gives employers an incentive to pay in non-money form. One such form is employer-provided health insurance. So an employer deciding whether to pay an employee an extra $100 in pay will realize that that costs him about $105 (see my earlier post for why it’s not $100 and why it’s not $107.65.) The after-tax benefit to the employee is about $72. So the “tax wedge” is about $28 plus $5 or $33.

This gives the employer and the employee an incentive to agree on a pay package that includes untaxed fringe benefits. The first $100 will be the most valuable. Then the next $100 less valuable, etc. Where will it stop? That is, at what point is the employer indifferent between paying in cash and paying in health insurance? Here’s the part I got wrong. It will stop when the value to the employee of an extra $100 is not $72, but $67.

But I also got something else wrong–on the infra margin. The hypothetical $15,000 that Arnold Kling discussed as an employer expenditure is not far off the mark. But I would be wrong to apply the 33% tax wedge to the whole thing. As I mentioned above, the first dollars spent on health insurance are worth more than the marginal dollars. So that value of that $15,000 to the employee, although it’s not $15,000, is more than 67% of $15,000. It’s only the last few dollars that are worth only 67%.