Case: U.S. Treasury Tax Rate Schedule

The U.S. Treasury's Office of Tax Analysis (OTA) has as its functions the evaluation of proposed changes to the federal tax law and the creation of tax-law proposals to support the President's policies. OTA is often requested to design a marginal-income-tax-rate structure that will yield a particular distribution of tax liability. The problem is characterized by the division of the tax-paying population into groups, usually on the basis of income. For each group of taxpayers, a target aggregate tax liability is specified and the tax schedule is designed to achieve this.

Tax Rate Schedules

The U.S. individual income tax code uses a marginal tax rate schedule. Each person's income is divided into brackets to which different rates are applied. In a ``four-bracket" hypothetical example, the first $10,000 earned is not taxed (the so-called ``zero-bracket"), the next $8,000 (all dollars earned above $10,000 but $18,000) is taxed at rate , the next $20,000 earned (between $18,000 and $38,000) is taxed at rate , the next $30,000 (between $38,000 and $68,000) is taxed at rate , and all income above $68,000 is taxed at rate . Hence an individual making $25,000 will pay in taxes, while someone earning $100,000 will pay taxes of .

Designing Tax Rate Schedules

The OTA is often given the job of identifying a tax schedule that will generate desired amounts of revenue for the government from different taxpayer groups. For example, Table 9 shows the total taxable income within four brackets by nine taxpayer groups. For example, all of the individuals in taxpayer group 5 are projected to earn $214B in income from bracket 1 and $2,072B of taxable income in bracket 2. The revenue generated (taxes assessed for government spending) from these people is billion dollars.

Policy makers have set revenue targets for each taxpaying group. For example, for group 5 in Table 9, it is desired that the $28,814B in revenues be acquired.

 
Table 9:  Four-bracket Tax Schedule Aggregates and Targets

Assignment

Using the data from Table 9 build and solve GAMS models for the following assignments.

1. Develop a goal-programming model to identify the best rate schedule. What assumptions were made regarding the structure of the rates?
2. Develop a goal-programming model that minimizes the sum of the squared deviations from the target revenues. How does this solution differ from the previous one?
3. How would the models above have to be modified to handle the following:
   1. Rate progressivity
   2. Integrality of rates
   3. Differentials between adjacent rates (minimum differences)
   4. ``Revenue neutrality," as required by President Reagan's tax reform program. The targets are the current taxes paid by the groups, and the new rate schedule should generate the same total amount of revenues to the government (tax increases for one group must be offset by reductions in another group).
4. How could a model determine both the bracket cutoffs and the corresponding rates?
5. If brackets were eliminated and a flat (single) tax rate was applied, determine: (a) the rate required to achieve the sum of the target revenues in Table 9, and (b) differences between the resulting group revenues and the target group revenues. (Note: most flat tax proposals have few deductions, taxing more income at a lower rate.) Is optimization needed to answer these questions?