In Transylvania the basic income tax system is fairly simple. The first 40,000 sylvers (the official currency of Transylvania) earned each year are free of income tax. Any additional income is taxed at a rate of \(25 \% .\) In addition, every individual pays a social security tax, which is calculated as follows: all income up to 80,000 sylvers is taxed at an additional \(20 \%\), but there is no additional social security tax on income above 80,000 sylvers. a. Calculate the marginal tax rates (including income tax and social security tax) for Transylvanians with the following levels of income: 20,000 sylvers, 40,000 sylvers, and 80,000 sylvers. (Hint: You can calculate the marginal tax rate as the percentage of an additional 1 sylver in income that is taxed away.) b. Is the income tax in Transylvania progressive, regressive, or proportional? Is the social security tax progressive, regressive, or proportional? c. Which income group's incentives are most adversely affected by the combined income and social security tax systems?

To calculate the marginal tax rates, first, we need to understand the taxes levied on different income levels. Income tax is charged at 0% for the first 40,000 sylvers and 25% for any amount above 40,000 sylvers. The social security tax is charged at 20% for all income up to 80,000 sylvers with no further tax applied to amounts above this. Given this information, let's calculate the marginal tax rates for incomes of 20,000, 40,000, and 80,000 sylvers: 1. 20,000 sylvers: Since this income is below the 40,000 sylvers threshold, there is no income tax. The social security tax is 20% of 20,000 which is 0.2 * 20,000 = 4,000 sylvers. The marginal tax rate is 4,000/20,000 = 20%. 2. 40,000 sylvers: There's still no income tax up to 40,000 sylvers. The social security tax is 0.2 * 40,000 = 8,000 sylvers. The marginal tax rate is 8,000/40,000 = 20%. 3. 80,000 sylvers: The income tax applies here. The first 40,000 sylvers are tax-free while the additional 40,000 sylvers are taxed at 25%, giving an income tax of 0.25 * 40,000 = 10,000 sylvers. The social security tax is 0.2 * 80,000 = 16,000 sylvers. The total tax is 10,000 + 16,000 = 26,000 sylvers. The marginal tax rate is 26,000/80,000 = 32.5%.

To determine if the tax systems are progressive, regressive, or proportional, we need to analyze the burden of taxes on different income levels. Progressive tax: The tax burden increases proportionally with income Regressive tax: The tax burden decreases proportionally with income Proportional tax: The tax burden remains constant across income levels - Income tax: The more you earn, the higher the income tax. This is a progressive tax system. - Social security tax: The tax is levied at 20% up to 80,000 sylvers and no further tax on income above 80,000 sylvers. Thus, the tax burden decreases as income increases, making it a regressive tax system.

To identify which income group has the most adversely affected incentives, we must compare the marginal tax rates. - Individuals earning 20,000 sylvers have a marginal tax rate of 20%. - Those with 40,000 sylvers have a marginal tax rate of 20%. - Lastly, individuals earning 80,000 sylvers have a marginal tax rate of 32.5%. Since the marginal tax rate is the highest for individuals earning 80,000 sylvers, their incentives are most adversely affected by the combined income and social security tax systems.