Megan McArdle addresses Laffer Curves and the marginal cost of public funds. I think this whole topic deserves much more attention but for now let me wax nerdy and just say that that Laffer Curves take average taxation on the X axis. This is really the only way to make sense of the typical shape. It is plausible to create utility functions such that maximum revenue occurs at 100% marginal taxation. More importantly there is really no reason to expect that revenues will go to zero at 100% marginal taxation. So to make the basic assumptions stick in general we have to be talking about average taxation.
Deadweight loss, however, is a purely marginal phenomenon. It is possible to have a 90% average tax rate and no deadweight loss if marginal taxes are zero along the relevant range.
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Thursday ~ June 18th, 2009 at 1:49 am
dWj
When taxes aren’t flat, it seems unlikely that revenues will depend only on the average tax rate; insofar as taxes are progressive, a more precise treatment isn’t going to be dealing with univariate functions. This is one of those simple illustrations that captures an effect that almost certainly exists in the real world without paying the least bit attention to all of the complications that (probably) don’t derail the argument. We can ask about a revenue-maximizing marginal tax rate on x at an income of y conditional on any number of other tax rates behaving as specified functions of our tax rate; in any reasonable situation, though, a full accounting is going to find a smaller change in revenue than if you assume that people don’t respond to the changes, and will find, at a high enough rate, that revenues decrease with rising tax rates. I think people dealing with the Laffer curve are almost always referring to marginal rates.
Thursday ~ June 18th, 2009 at 1:39 pm
kwsmith2
No doubt that revenues depends on the structure as well as the average rate.
However, the basic formulation of the Laffer Curve says that at 0% tax there is no revenue and at a 100% tax there is no revenue, so the maximum tax must occur somewhere in between.
It, however, is not true that a 0% marginal rate will yield no revenue nor that a 100% marginal rate will yield no revenue. So while I think most people use the Laffer Curve to justify changes in the marginal rate, thats not consistent with the basic formulation.
Monday ~ June 22nd, 2009 at 5:38 pm
Tim Fowler
RE: “It is plausible to create utility functions such that maximum revenue occurs at 100% marginal taxation. ”
You could make a graph of such a function, but it wouldn’t be very plausible as an explanation of the real world.
Re:” It is possible to have a 90% average tax rate and no deadweight loss if marginal taxes are zero along the relevant range.”
If you have a 90% average effective tax rate, your not going to have a situation where everyone faces 0% tax on their next dollar.
And while marginal tax rates are likely the most important issue with the loss from taxes they aren’t the only issue. Its reasonable to assume that at least by the time you reach 90% tax rates the government is not using the money to efficiently meet the real needs and desires of people as they would with their own money. Also its almost certain that the tax will distort investment in some way or another even if it is explicitly and carefully designed to avoid that, and esp. if its the normal creation of the political process.
Kwsmith2 – It is true that either marginal rate may not produce zero revenue, but and effective tax rate of 0 or 100 percent will produce no tax revenue. 0% of anything is zero. And if the government takes 100% then there is nothing left for corporations or individuals. Even giving them money for food (or just the food directly) means the government is taking less than 100%.