# Dynamic Calculations and the Entitlement Crisis

7/17/08

Everybody is now familiar with the idea (generally attributed to Laffer) that tax rates have a revenue maximizing point. If they are raised beyond this point, government revenue actually falls in the near term.

However, the tax rate that maximizes long term government revenue will be far lower still. This is because if tax rates are reduced below the revenue maximizing point, the economy grows faster. As the economy grows, the tax base in future years is increased. The effect compounds year over year, so that if the tax rate were to be set so as to maximize the present value of total future government revenue, it would clearly be set much lower than the immediate revenue maximizing rate.

Alternatively, if the government knew it had pension obligations coming up that it needed to find a way to pay for, it should cut taxes well below the revenue maximizing rate now, so as to grow the tax base as rapidly as possible. What the government historically has done instead, raising social security taxes beyond immediate needs to build up a "trust fund", is the exact opposite of this and has compounded the problem.

The economy can be compared to an Individual's Retirement Account. One sensibly defers immediate consumption to contribute to one's IRA. Because taxes are not paid on the investments each year in an IRA, the investments compound rapidly. This allows one to retire comfortably. The government effectively invests in the tax base if it allows money to compound in the private sector rather than spending it now. Since each 1% of taxation that the government takes imposes additional dead weight penalties on the economy, this investment can be amazingly productive in the long run.

The revenue maximizing rate, by definition, is the point at which a reduction of 1% in the tax rate will keep the government's take constant in the next year, meaning that such a reduction will cause national income to increase by 1/r %, where r is the revenue maximizing tax rate. If r is 25%, for example*, national income will increase by 4% if the government cuts taxes from 25% to 24%, which would thus cost the government no immediate revenue. Some of that 4% will be a one time constant factor, but a sizeable fraction of it (how much will depend on model details) is sustainable growth that will recur year upon year. So at this revenue maximizing point, cutting the tax rate 2%, with essentially zero loss in immediate government revenue, might contribute to a 2% rise in growth, which compounded 20 years would yield a 50% bigger tax base. A rate cut to 15%, instead, would cost the government significant revenue in year 1, but could much more than make up for it over a 20 year span.

While the precise rate that optimizes long term government revenue may depend on the details of one's model, one conclusion is so robust as to be essentially model independent. Any tax cut that does not substantially lower government revenue in the first few years, is not deep enough to maximize long term government revenue. The prudent course is to continue cutting until sustained revenue losses are incurred.

There are reasons to believe current tax rates are near or above the rate that would maximize government revenue next year. But they are surely far above rates that would maximize government revenue over the next 20 years. If the government were serious about dealing with its entitlement obligations, it would immediately slash taxes and spending.

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Eric Baum