12.2 State Tax Refrom

You were just elected state governor. The central promise of your election campaign was to reform the state’s tax system to make it more progressive. There are ten households in your state and each spends their money on three items: Gasoline, food, and other goods. There are large variations of income and spending patterns across the three categories in your state. Let \(M\) represent the income of the household. The prices for gasoline, food, and other goods are \(P_{GAS}\), \(P_{FOOD}\), \(P_{OTHER}\), respectively. The quantity demanded (i.e., \(Q_{GAS}\), \(Q_{Food}\), and \(Q_{OTHER}\)) of each households depends on the demand parameters \(\alpha_{GAS}\), \(\alpha_{FOOD}\), and \(\alpha_{OTHER}\). The demand functions can be written as follows. \[Q_{GAS}=\frac{\alpha_{GAS}}{\alpha_{GAS}+\alpha_{FOOD}+\alpha_{OTHER}}\cdot \frac{M}{P_{GAS}}\] \[Q_{FOOD}=\frac{\alpha_{FOOD}}{\alpha_{GAS}+\alpha_{FOOD}+\alpha_{OTHER}}\cdot \frac{M}{P_{FOOD}}\] \[Q_{OTHER}=\frac{\alpha_{OTHER}}{\alpha_{GAS}+\alpha_{FOOD}+\alpha_{OTHER}}\cdot \frac{M}{P_{OTHER}}\] Besides the demand functions, the following information characterize your state’s tax system:

• State income tax rate measured in % of household income
• State sales tax rate (in %) added to the price of food and other goods. The sales tax is is not applied to gasoline.
• Gasoline tax in dollars per unit of quantity demanded.

You can obtain the retail prices (relevant for the demand equations) by applying the taxes to the wholesale prices. Before considering any options to reform the tax system, you must calculate the current tax expenditures and effective tax rates to obtain a baseline. You are considering various options to reform the tax system to make the overall taxes more progressive:

• Exempting food purchases from the sales tax and uniformly (i.e., for all incomes) raising the income tax
• Exempting food purchases from the sales tax and increasing the income tax for households above a certain threshold
• Lowering the gasoline tax and uniformly (i.e., for all incomes) raising the income tax

There are certain constraints associated with all those scenarios.

• You cannot change the sales tax rate and gasoline tax by household. Those taxes have to be changed for all households.
• The revenue generated across all four tax revenue streams cannot decrease. That is, the state is providing services that are paid for by the tax revenue.

Since you are a politician and are already thinking about re-election, the case study should include the number of people who are better and worse off under the various regimes. The write-up of the case study should evaluate the baseline and three scenarios in terms of progressiveness of the tax as well as impact on the households compared to the baseline. Evaluate the advantages and disadvantages of all scenarios.