Monday, March 14, 2005

Tax Code: Economic Goals

It is important we figure what our goals are:

1. Take in a great deal of revenue for our government (government spending is about 4% of GDP)
2. Be progressive. We are aware that people with less money need their money more, even if we disagree on the degree.
3. Be efficient. To not hurt the market, or encourage perverse behavior (like black markets).
4. Be malleable for technocratic aims. Targetted tax cuts and penalties are a useful function the government can use, assuming we can trust our democratic representatives at all.

These are not all hard and fast rules, just various costs and benefits to consider. We must keep in mind that advancing in one goal often has draw backs in others. The ideal tax code finds the diminishing returns we can get from each of these. I think ideologues on both sides need to recognize that these are separate and often competing goals. We are probably not at the current optimum, but reaching that optimum does not require just moving in 1 direction on 1 goal.

For instance, I am in favor of a small sales tax. I am well aware of how regressive a sales tax is, because the lower you are on the economic scale, the greater a fraction of your spending you consume. But let’s look how much inefficiency can be erases.

In the traditional supply demand curve, the points where supply and demand intersect, is the set price, and the large triangle below the demand curve before that point and above the supply curve, is the surplus generated. Economists and technocrats generally want to maximize this surplus as much as possible, whether it is surplus that goes to producers, workers, consumers, or the government even.

So let’s add a tax on the supply curve. Just a fixed increase of X on each marginal unit, so we draw a parallel line to the supply curve, a little higher. The causes a higher set price. There’s much less surplus between consumers and producers now, but most of that is government income, which is fine.

The deadweight loss is the little bit cut off the nose of the triangle. That would be the people who were somewhat undecided about buying or selling before, and now that the tax has added costs, it’s not worth the trouble. This is small, but it’s the only inarguable bad part of government taxation. Deadweight triangle.

Note, the size of this triangle is directly a function of tax level X, something on the order of X squared. (in this idealized picture, around 1/3 x^2). Such an increase in the inefficiency of X, means we are pretty concave for X (ie, we’d rather two taxes at half the level than one tax at that level).

Now take two different markets side by side. Your government needs to bring in a certain amount of revenue, let’s say T. So the tax on both markets needs to add up to that, or X + Y = T. Your inefficiency loss is going to be X^2 plus Y^2. Pretty clearly, having X and Y at the same level is much better than having only X market be taxed, in fact it creates about ½ less inefficiency. This is great.

One would extrapolate from that, that “double taxation” complaints are BS. In order to generate as little inefficiency as possible, you should have as many taxation methods as possible. The total tax load could still be small or big, but the number of methods you use are still important. Idealistic notions of just taxing one form of wealth (property, or consumption, or tariffs or …) are extremely inefficient, why pundits shouldn’t be in charge of technocratic policy.

Of course the sales tax is still regressive, but there has got to be points where the amount it is relieving the extremely high inefficiencies elsewhere that balances out regressive effects. Not to mention the rest of your tax code (such as income, savings, and property taxes) can be engineered to balance and create overall progressive codes.

Math is fun.


At 9:47 PM, Anonymous said...

so, i don't actually have anything intelligent to say, but i just wanted to note that i really enjoyed reading this.


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