Question

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?

Short answer

Answer: The incentives of individuals earning 80,000 sylvers are most adversely affected by the combined income and social security tax systems, as they have the highest marginal tax rate of 32.5%.

Step-by-step solution

a) Calculation of Marginal Tax Rates

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%.

b) Progressive, Regressive, or Proportional Taxation

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.

c) Income group with most adversely affected incentives

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.

Key concepts

Marginal Tax Rate

The marginal tax rate is an important concept in taxation. It represents the proportion of an additional unit of income that is paid in taxes. This helps to understand how much extra tax one would pay when earning an additional sylver. In the Transylvanian tax system, the calculations show how the marginal tax rates depend on income levels.

• For incomes up to 40,000 sylvers, only the social security tax applies, resulting in a marginal tax rate of 20%.
• However, at 80,000 sylvers, additional income triggers both a 25% income tax and the same 20% social security tax.

Hence, the marginal tax rate jumps to 32.5% when you take these additional taxes into account.

Income Tax

Income tax in Transylvania has a simple structure. It only kicks in when income exceeds 40,000 sylvers. This means, up to this point, there is no income tax, but once earnings go beyond this limit, the additional income is taxed at a flat rate of 25%.
It is important to know that the term 'income tax' refers to the tax that is directly related to one's income level. As seen in the exercise,

• 0% tax rate until earnings reach 40,000 sylvers.
• 25% tax rate on any earnings above this amount.

This design ensures that higher income earners contribute more, marking the income tax as progressive.

Social Security Tax

Social Security Tax is levied to fund the social security system in Transylvania. Here, this tax is more complex because it behaves differently across income levels. Regardless of how much a person earns, the first 80,000 sylvers are taxed at a rate of 20%. This is capped, meaning income over 80,000 sylvers is not subject to this tax.
The breakdown is as follows:

• 20% tax applies up to 80,000 sylvers.
• No further tax beyond this income level.

This creates a unique situation where, contrary to the income tax, the social security tax exhibits regressive characteristics as income rises above 80,000 sylvers.

Regressive Taxation

Regressive taxation is a system where the tax burden decreases as income increases. In the context of Transylvania’s tax system, the social security tax is regressive. This is because higher earners experience a lower average tax rate once their income exceeds 80,000 sylvers, as no additional social security tax is applied past this point.
Unlike a progressive system, where higher income earners pay a higher proportion of their income in taxes, a regressive system like this social security tax can appear skewed in favor of wealthier individuals.
Understanding this dynamic is crucial, as it implies that lower-income individuals pay relatively more in taxes proportionally compared to high-income earners, thereby imposing a higher relative tax burden on them.