### Why Casey Mulligan is wrong about everything

**Matthew Martin**8/15/2013 12:11:00 PM

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I won't dispute Mulligan's claims over the existence of these "taxes" and their incentive effects (though someone should). Suppose he's right about that, here's a simpleton argument why he's wrong about everything else:

Consider a standard microeconomic model. Household utility is thus: $$U=ln\left(c\right)+ln\left(1-L\right)$$ with a budget constraint of $$c\leq \left(1-\tau\right)wL+\theta$$ Maximizing utility, the household chooses labor supply $L$ according to $$L=\frac{1}{2}-\frac{\theta}{2\left(1-\tau\right)w}$$ Note that the expression $\left(1-\tau\right)w$ is just a way of writing the worker's after-tax wage rate (lets call the after tax wage $w_{at}\equiv \left(1-\tau\right)w$ , and that the worker really doesn't care at all about the tax rate per se. That is, the worker is indifferent between being paid $w$ at a tax rate of $\tau$ versus being paid $w_{at}$ with no taxes. Furthermore, note that the after-tax wage nearly falls out of this equation--when $\theta=0$, taxes have no effects on the employment supply decision (ok, implicit assumptions of the maximization procedure required an interior point--at the boundary point of a 100 percent tax rate, this labor supply equation does not hold).

What is $\theta$? It refers to the profits the household gets from ownership of firms. To the extent that firms are perfectly competitive, $\theta=0$. The point is that $\theta$ is generally small--most people don't have huge streams of income other than their wages.

Why do I bring up such a simplistic model when you could easily reverse the result with a more complicated one? Because it appears to be basically right:

The result holds.

My point is this: analytically, lower effective marginal taxes is identical to higher wage rates, so rising wages due to productivity growth should have identical effects to cutting taxes. So why hasn't the labor supply exploded?

Economists often fall victim of incentive-worship, whereby an economist considers only the effect of prices on substitution, and not the effect of prices on wealth. Mulligan's whole argument presumes that the substitution effect--whereby lower after-tax wages decrease labor supply--is always much larger than the wealth effect--whereby lower after-tax wages induce people to work more to make up the difference. In reality, what we see is that for the most part the two effects balance out, so that doubling wages had very little effect on labor supply--in fact it decreased.

So lets revisit Mulligan's hypothesis. Let's suppose that the ACA imposes massive new hidden taxes, amounting to 50 percent of your disposable income. That implies that the average weekly hours will be at 1960s levels--5 hours a week more than we are currently working!

Thus, for the most part, substitution effect=wealth effect. This has to be a fairly robust result, because labor supply is always bounded--there are only 24 hours in a day. And, we know of a utility function of which this is true. It's called cobb-douglas. Perhaps Casey Mulligan has heard of it?