## Tuesday, June 27, 2006

### Consumption vs Income Taxation

In a previous post, I expressed a preference for consumption taxation over income taxation. In a comment, Daniel Demetri (an ec 10 student this past year) asks an important question about incentives:

I'm confused as to why a consumption tax does not affect incentives while an income tax does.... People don't care about saving money--they care about spending it.

With income tax: 1 hr work --> \$16 pre-tax --> \$8 post-tax --> \$8 of chocolate cake, video games, and Red Sox tickets.

With consumption tax: 1 hr work --> \$16 pre-tax --> \$8 of chocolate cake, video games, and Red Sox tickets + \$8 of tax.

The amount worked and the amount spent are the same, so what's the real difference?

Daniel is exactly right, as far as he goes. If we are looking at the decision to work today in order to consume today, consumption and income taxes have similar effects. Both discourage work effort.

Consider, however, another margin of adjustment: Work today in order to save and consume in the future. Let's continue with Daniel's example of a 50 percent tax rate. Suppose that the interest rate is 7 percent, so \$1 saved today becomes \$2 in 10 years.

With income tax: 1 hr work --> \$16 pre-tax --> \$8 post-tax --> \$16 of savings in 10 years --->\$4 more in income taxes on the interest--> \$12 of chocolate cake, video games, and Red Sox tickets.

With consumption tax: 1 hr work --> \$16 pre-tax --> \$32 of savings in 10 years --> \$16 of chocolate cake, video games, and Red Sox tickets + \$16 of tax.
So under a consumption tax, there is a greater incentive to work and save today in order to consume in the future.

Let's be even more wonky about this and do a bit of math. Let W be the real wage, r be the interest rate, and t be the tax rate. Suppose I work today in order to save and consume in T years. Under an income tax, the amount of consumption I get for one hour of work is:

(1-t)W*[1+(1-t)r]^T

Under a consumption tax, the amount of consumption I get is:

(1-t)W*[1+r]^T

Now compare these after-tax relative prices to the before-tax relative price, which is

W*[1+r]^T

You can see that the consumption tax creates a constant wedge: the after-tax relative price is 1-t times the before-tax relative price, regardless of T. However, an income tax creates a growing wedge. The larger is T, the greater is the gap between the before-tax and after-tax relative price. In other words, a consumption tax taxes current and future consumption at the same rate, whereas an income tax in effect taxes future consumption at a higher rate than current consumption.

The bottom line: Both consumption taxes and income taxes discourage work, but income taxes discourage saving as well.