The key assumption to this assertion is continuity of the economic output as a function of tax rate. So let's examine source of discontinuities:
First, the economy as a whole is not subject to a single tax rate. The main sources of revenue for the government are (in order) personal income taxes, employment taxes, and corporate taxes. Each of these has a different tax structure, and so each type of tax will have its own set of economic curves.
-Personal income taxes are progressive. This means that individuals have different effective tax rates, depending on AGI. If you plot the AGI versus effective tax rate, you will see a discontinuous curve.
-Employment taxes are discontinuous because they are capped-you do not pay them above a certain amount of income.
-Corporate taxes are generally paid on profits, not revenue. Thus, GM can produce billions of dollars of product and not pay tax.
It is obvious that each of the major tax elements is discontinuous. Does that invalidate the Crier Curve analysis? I don't know. The Crier curve is a macro phenomenon, while each of these effect is a micro phenomenon. One analogy is to the Ideal Gas Law, which states that the relationship between pressure, volume, and temperature in a closed system is described by:
Pressure x Volume/Temperature = Constant
Temperature is a macro phenomenon that is an aggregation of the thermal kinetic energy of the gas molecules. Each molecule will each have its own energy function over time, and trying to describe their interactions on a molecular level is impossible. However, it does not matter because we have the macro level concept of temperature.
In the same manner, a variety of variables go into a person's economic output. These include education, intelligence, skills, luck, personal motivations, risk aversion, what company you work for, and other factors. Similarly, a lot of factors go into an individual's effective tax rate. For example, itemized deductions establish a baseline below which the tax rate is zero. Marital status affects one's tax rate.
A corporation's effective tax rate depends largely on profitability. The higher its profits, the larger its effective tax burden.
Thus, on the micro level, you have over a hundred million individuals and tens of thousands of companies, each with the possibility of contributing to the economy and the tax base. My intuition says that these aggregate to a continuous economic output as a function of the tax rate; the discontinuities cancel or are otherwise inconsequential.
Regardless, I still think that the fundamental hypothesis holds:
The aggregate tax rate of an economy can be optimized at one of three different tax rates:
-A low tax rate that maximizes the wealth retained by the private economy.
-A middle tax rate that maximizes the size of the overall economy.
-A high tax rate that maximizes government revenue.