This lengthy blog analyzes a simple case in order to argue that Rothbard is correct on the issue of income vs. consumption tax. The last portion of it suggests that Cain’s proposal is a Trojan Horse and that Ron Paul is the only candidate with the courage to address the main issue: the size and power of government itself. How the government finances itself by taxes is distinctly secondary to the power to tax us in the first place.

Let’s analyze this issue of income vs. consumption taxation in the simplest possible way. Two people inhabit an island. Person P produces 5 fish a day. Person T has the power to tax person P by taking one fish from P’s take. This is a lump-sum income tax. P is unable to hide any fish and T taxes P without any cost of taxation, i.e., assume no tax evasion and no costs of collecting the tax. There is no explicit pricing of the fish. Assume that P and T both live one period and then die. All of this is certain.

Assume that P consumes all 5 fish a day prior to the appearance and taxation of T. P’s income is 5 fish a day at each of two periods and his consumption is also 5 fish a day. T appears and announces the income tax. P must comply (by assumption). Fighting, escape and counter-measures are ruled out.

In order to optimize, P works up to the point where the disutility of spending time fishing (working) equals the utility of getting a fish to eat.

P has two options. First, he can work harder each period to produce 6 fish a day, one of which he hands over to T. If he does this, the income tax is a tax on his leisure time. His consumption is unchanged. He will do this if the additional disutility of work (the marginal disutility of work) is less than the additional utility of consumption. Second, he can work the same time, producing 5 and consuming 4. He does this if the marginal disutility of working to produce a sixth fish exceeds the marginal utility of consuming one fish fewer. (A third option, which is to produce 4 fish and consume 3, doesn’t appear to be rational.) In this case, the tax manifests itself as a tax on both income and consumption.

If T knows P’s utility function, then he can set a tax rate instead of a lump-sum tax of one fish. If he knows that P wants to produce and consume 5 fish net of tax, then he sets the income tax rate at 16.67 percent. When P produces 6 fish. he then gives up one and consumes the other 5. If he knows that P wants to work only enough to produce 5 fish, then he sets the income tax rate at 20 percent.

Now we analyze a consumption tax. T wants to take one fish. T has to choose a tax rate t such that t x C = 1 fish, where C = P’s fish consumption. P has to find it rational to produce C + tC fish and hand tC fish over to P, where t C = 1. Therefore, t = 1/C. The way that this tax works is that after P consumes some fish, he then is forced to work enough additional time so as to produce one fish for T. If P consumes 5 fish, he must work enough to generate one more fish for T. The consumption tax is 20 percent of the fish consumed. His implicit income tax rate via this consumption tax is 1/6 = 16.67 percent. T sets the consumption tax at this rate. If P consumes 4 fish, then he must work to produce 5 fish. Then T sets the consumption tax at 25 percent, and the implied income tax rate is 20 percent.

T has to know P’s utility for work and leisure when setting the consumption tax rate so as to net himself one fish. He also needed to know that in order to set an income tax rate.

I’ve made T’s taxation a given amount, one fish, and then showed at what rates T can get what he wants. The idea is that this represents a fixed amount of government spending. T will take and eat that one fish, and he wants to set either an income tax or a consumption tax that achieves that result. He can use either tax, a consumption tax or an income tax. They both come down to a tax on P’s labor for his benefit. This is simultaneously a tax on P’s leisure, since labor time takes away from leisure time.

In this modeling of the taxation, Rothbard is correct. The intuition is that the tax man can get a given take by either means, income or consumption, by adjusting the tax rates. The size of the tax man’s spending is the tax. The nature of the tax and the rates chosen to achieve the tax are a matter of indifference to the taxpayer P in this simple model.

Suppose that we allow two time periods and suppose that P is able to postpone consumption by storing fish for one period. This may have utility for him, in which case there is an implicit rate of return or yield from storage. Suppose, for example, that P can work harder and easier when he is younger. He prefers to produce 6 fish in period one of which he saves one and consumes 5. In period two, he produces 4 fish and saves none. He then consumes 5 fish, consisting of the 4 from period two production and the one that he saved.

Along comes T who wants some of P’s fish. His taxation policy depends on what sort of consumption through time that he prefers. He too can save and store fish. What he will do is tax P more heavily in period one and save fish for later consumption. It seems intuitive that if he knows P’s utility function he can select either consumption or income tax rates to achieve his tax take.

The type of tax starts to matter both to producers and government when we allow more than one producer, each of whom has different utility functions. Further complication arises when each producer has distinctive production opportunities and obtains finance from other savers. A single tax rate then affects different producers differently. To produce a given take, the tax man will have to discriminate among producers by imposing different tax rates and using different kinds of taxes. The costs of tax evasion are another realistic factor.

However, even if they matter, all that this does is get people arguing with one another and fighting one another over who is going to work to pay the taxes. These disputes cloud a larger issue, which is the overall size of the taxes, and even that is not the main issue. Government spending has to be coming out of the work product of Americans. It is the best single measure of total taxes that we have. Government spending is the main issue. It’s the main issue, in my view, because it’s so enormously wasteful and destructive.

In my opinion, any new form of taxation of Americans, such as a value-added tax or a national sales tax, under the guise of saving the system or balancing the federal government’s budget, is a Trojan Horse. It should be strongly and immediately rejected by Americans. It is only going to enslave us further. Cain’s plan and any similar plans will end up raising taxes and thereby assuring that government spending is not cut.

Ron Paul has had the courage to recommend eliminating five government departments. That’s for starters. He has the correct focus. That results in tax cuts. That results in more freedom. That results in less waste and less destruction of productive opportunities.

Getting worked up over different forms of taxation is a diversion from the main issue, which is the power of government to tax in the first place and then use the resources forcibly extracted from laborers (producers) so wastefully.

3:06 am on October 22, 2011 Email Michael S. Rozeff