Wednesday, April 18, 2012

The art of caricature


To get insights about the real world, consider extreme (even unrealistic) cases.
Stage 1: Consider extreme cases. Don’t care about realism at this stage.

Stage 2: Would some of the features of your extreme cases subsist in less extreme cases? Does that give you an insight about the real world? If yes, that’s nice. If not, that was a nice try.

This trick might give you some idea about what may actually exist. More work is usually needed to prove that it can in principle actually exist, and even more work is necessary to prove empirically that it actually exists. This trick never shows that something cannot exist (if your extreme cases do not have some property, that doesn’t prove that this property will necessarily be absent in all other cases).

If a parameter is crucial for the question you have to answer, it might be useful to try extreme values of this parameter, even when they are unrealistic.

What impact does a reduction of tax rates on labor income have on how much workers want to work?

Stage 1:  What happens if the tax rate is originally equal to 100% (this means that workers have to give up their whole labor income to the state)? Obviously workers won’t work (assuming away the interest for the job, other kinds of reputational compensation, or any social pressure). Then, assume that the tax rate is reduced, let’s say to 20%. Will workers work? It depends on how rich they are. Let’s say they receive some money from the state (do not consider where the money comes from; maybe the state has a sovereign fund financed in the past by selling a huge amount of diamonds). If what they receive barely suffices to survive, they will be likely to work when the tax rate is reduced to 20%. If each worker receives billions of dollars each year, and their labor incomes would be tiny in comparison, it is likely that they will not work. Thus while lowering the tax rate will tend to encourage workers to work more, having a higher income will reduce their motivation to work more.

Stage 2:  The insight is that reducing tax rates may, but will not necessarily, motivate workers to work more. Income has to be taken into account. What would happen if we started with a tax rate under 100% (for example 30%)? In the real world, we can forget about workers receiving huge amounts of money from the state. They will already be working before the tax reduction, and thus paying taxes. This means that the tax reform would make them richer even if they do not change their work load, because they would keep more of their labor income. Thus, two variables are changing simultaneously: the tax rate and the income of workers. And it may well be the case that these two variables have opposite incentives on work (as in our extreme case). We cannot yet be sure that these variables will generate the same incentives in the general case as in our extreme case, but this might be a possibility.

By the way, a tax rate of 100% is not as unrealistic as it sounds. This would happen if the state guaranties some minimal revenue by transferring the difference to workers who earn less than that. In this case, if the worker earns 100 dollars more but stays under the threshold, she will still have the same total income (labor income + transfers). This means that, for her, the tax rate is 100%. Thus, she has no incentives to work more (as long as she stays under the threshold). That’s called the “poverty trap”. Thus a tax rate of 100% is not necessarily unrealistic, but considering that extreme case would have been useful even if it were completely unrealistic.

What may be the impact of rent controls?

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