Taxes are collected for two basic purposes: to provide public goods such as national defense and a legal system and to redistribute income.

Over some range of taxation, the provision of government goods and services makes private economic activity more productive. For example, America's current level of productivity would not be possible without the infrastructure, protection of property and educational level of the workforce we have. Thus, up to some level, reducing private goods by a dollar yields more than a dollar increase in total output. Beyond some point, especially when taxes are used mainly for transfer payments, they reduce incentives to produce enough that they lower the rate of economic progress. Then, reducing private goods by a dollar yields less than a dollar increase in total output.

Using an economic model, we find a tax rate that will maximize economic growth. A higher tax rate will result in a loss of potential output for society as a whole. Using data for the 46-year period from 1950 through 1995, the model finds:

• The tax rate that would have maximized economic growth for the United States is 21 percent of gross domestic product (GDP); this tax rate would have produced average annual real economic growth of 4.8 percent.

• However, taxes took 24.2 percent of GDP in 1950 and continued to rise thereafter; as a result, the actual growth rate over the period averaged only 3.4 percent.

The additional 1.4 percentage points of growth would have resulted in workers now producing (measured in 1992 dollars) $107,900 in per capita output instead of $54,100. This means that the average person would have twice the real income he or she has today. The resulting increase in taxes paid could have paid for all government programs and left the nation debt free!

If the 21 percent tax rate had been in effect, cumulative real GDP (measured in 1992 dollars) during 1950-95 would have totaled $88 trillion more than the actual $173.5 trillion.

• On the average, each dollar of tax collected caused a $1.71 loss of private wealth over the 46-year period.

• However, the higher the tax burden, the higher the cost to the economy; specifically, each additional dollar of tax is causing a loss of $3.44 of GDP (output that was never produced).

A tax rate well above the optimal rate is common among other industrialized nations as well. The resulting loss in a number of other countries for which data are available has retarded economic growth in those nations, too.

• On the average, the growth-maximizing tax rate is about 20 percent of GDP among developed countries - ranging from 16.6 percent for Sweden to 25.2 percent for the United Kingdom.

• Current levels of taxation, however, range from 34.1 percent in the United Kingdom to 51.6 percent in Denmark.

• The marginal cost of taxation for each unit of local currency is 5.70 in Denmark, 3.34 in the United Kingdom, 1.59 in Italy, 4.20 in Sweden, 1.76 in Finland and 3.43 in New Zealand.

Not only would Americans have a higher standard of living if the tax rate had been at 21 percent of GDP, but based on public spending and indicators of social progress, it appears that the marginal benefit of taxation in the United States has been far less than the marginal cost. There is evidence that government spending prior to 1960 led to measurable improvements in social indicators. However, the explosive growth in government spending after 1960 has been accompanied by only modest improvement.

Many European nations take an even higher percentage of GDP in taxes than does the United States. Their experience suggests that in any economy where the marginal cost of taxation exceeds the marginal benefit, the eventual result is lower economic growth, reduced job formation and increased unemployment.