Question

Use the following table to work Problems 7 and 8 The table shows three redistribution schemes. $$\begin{array}{cccc} \begin{array}{c} \text { Before-tax } \\ \text { income } \\ \text { (dollars) } \end{array} & \begin{array}{c} \text { Plan A } \\ \text { tax } \end{array} & \begin{array}{c} \text { Plan B } \\ \text { tax } \end{array} & \begin{array}{c} \text { Plan C } \\ \text { tax } \\ \text { (dollars) } \end{array} \\ \hline 10,000 & 1,000 & 1,000 & 2,000 \\ 20,000 & 2,000 & 4,000 & 2,000 \\ 30,000 & 3,000 & 9,000 & 2,000 \end{array}$$ Which scheme has (i) a proportional tax? (ii) a regressive tax? (iii) a progressive tax?

Short answer

(i) Plan A is proportional. (ii) Plan C is regressive. (iii) Plan B is progressive.

Step-by-step solution

Understand Tax Schemes

First, understand the types of tax schemes: Proportional tax takes the same percentage from all incomes, regressive tax takes a smaller percentage from higher incomes, and progressive tax takes a larger percentage from higher incomes.

Analyze Plan A

Plan A has the following taxes: \[ \text{For } 10,000: 1,000 \text{ tax} \text{For } 20,000: 2,000 \text{ tax} \text{For } 30,000: 3,000 \text{ tax} \] Calculate the tax rate by dividing the tax amount by the before-tax income. \[ \frac{1,000}{10,000} = 0.1 \text{ (10%)} \frac{2,000}{20,000} = 0.1 \text{ (10%)} \frac{3,000}{30,000} = 0.1 \text{ (10%)} \] Plan A deducts a constant 10% from every income, indicating a proportional tax.

Analyze Plan B

Plan B has the following taxes: \[ \text{For } 10,000: 1,000 \text{ tax} \text{For } 20,000: 4,000 \text{ tax} \text{For } 30,000: 9,000 \text{ tax} \] Calculate the tax rate: \[ \frac{1,000}{10,000} = 0.1 \text{ (10%)} \frac{4,000}{20,000} = 0.2 \text{ (20%)} \frac{9,000}{30,000} = 0.3 \text{ (30%)} \] Plan B applies a higher tax rate as income increases, indicating a progressive tax.

Analyze Plan C

Plan C has the following taxes: \[ \text{For } 10,000: 2,000 \text{ tax} \text{For } 20,000: 2,000 \text{ tax} \text{For } 30,000: 2,000 \text{ tax} \] Calculate the tax rate: \[ \frac{2,000}{10,000} = 0.2 \text{ (20%)} \frac{2,000}{20,000} = 0.1 \text{ (10%)} \frac{2,000}{30,000} \text{ approximately equals } 0.067 \text{ (6.67%)} \] Plan C deducts a fixed amount regardless of income, leading to a higher percentage from lower incomes, indicating a regressive tax.

Key concepts

Proportional Tax

In a proportional tax system, everyone pays the same percentage of their income, regardless of how much they earn. This means that the tax rate remains constant. The key point here is that as income increases, the absolute amount of tax paid also increases, but the proportion or percentage of income paid as tax stays the same.
For example, if the tax rate is 10%, a person earning \(10,000 would pay \)1,000 in taxes, and someone earning \(30,000 would pay \)3,000 in taxes.
The proportional tax system is often seen as fair because everyone pays the same rate. However, it can be argued that it does not take into account the varying ability of individuals to pay, as those with lower incomes might find it harder to part with the same percentage of their income.
In the given exercise, Plan A is an illustration of a proportional tax system, as every income level is taxed at a constant rate of 10%.

Regressive Tax

A regressive tax system places a higher relative burden on lower-income earners than on higher-income earners. This means that as your income increases, the percentage of your income paid in taxes decreases.
For instance, if there's a \(2,000 flat tax, someone with an income of \)10,000 would pay 20% of their income in taxes, while someone earning \(30,000 would pay approximately 6.67%.
Critics argue that regressive taxes are unfair because they disproportionately affect those who can least afford them. They can exacerbate income inequality by taking a larger share of income from those with lower earnings.
In our exercise, Plan C is an example of a regressive tax system. Here, everyone pays a fixed amount of \)2,000 in taxes, resulting in lower-income individuals paying a higher percentage of their income compared to higher-income individuals.

Progressive Tax

In a progressive tax system, the tax rate increases as income increases. Higher-income earners pay a larger percentage of their income in taxes compared to lower-income earners.
For example, in Plan B of the given exercise, you would pay 10% on a \(10,000 income, 20% on a \)20,000 income, and 30% on a $30,000 income. A progressive tax system is designed to ensure that those who have greater financial capacity contribute more to the funding of public services and infrastructure.
Supporters argue that progressive taxes are fairer because they lessen the burden on those who have less ability to pay and require more from those who can easily afford it. However, critics might argue that progressive taxes can discourage investment and economic growth by imposing higher taxes on those with greater financial resources.
As illustrated in Plan B, a progressive tax plan adjusts the tax rate according to income levels, making it a common choice in many countries seeking to reduce income inequality.