AS Level Economics 9708: Progressive Income Tax, Average Tax Rate and Transfer Payments

A government uses the following simplified income tax system to help redistribute income: the first $10,000 of a person's annual income is tax free; income from $10,000 up to $30,000 is taxed at $20\%$ ; and any income above $30,000 is taxed at $30\%$ .

Amara earns $20,000 per year and Boas earns $50,000 per year.

(a) Calculate the total tax paid by Amara and by Boas under this system, showing your working for each. [4]

(b) Calculate each person's average rate of tax (the tax they pay as a percentage of their total income). [2]

(c) Using your answers to (a) and (b), state and explain whether this income tax system is progressive, proportional or regressive. [2]

(d) Explain what is meant by a "transfer payment", giving one example, and explain one difference between a transfer payment and the income tax system above in how each affects the distribution of income. [2]

Part (a): Total tax paid by Amara and Boas

The tax system has three bands: $0 tax on the first $10,000, $20\%$ on income from $10,000 to $30,000, and $30\%$ on any income above $30,000.

Amara (income $20,000). The first $10,000 is tax free. The remaining $10,000 of her income (from $10,000 up to her total of $20,000) falls in the $20\%$ band: $20\% \times 10{,}000 = 0.20 \times 10{,}000 = 2{,}000$ Amara’s total tax is $2,000.

Boas (income $50,000). The first $10,000 is tax free. The next $20,000 (from $10,000 to $30,000) is taxed at $20\%$ : $20\% \times 20{,}000 = 0.20 \times 20{,}000 = 4{,}000$ The remaining $20,000 of his income (from $30,000 up to his total of $50,000) is taxed at $30\%$ : $30\% \times 20{,}000 = 0.30 \times 20{,}000 = 6{,}000$ Boas’s total tax is $4{,}000 + 6{,}000 = 10{,}000$ , i.e. $10,000.

Part (b): Average rate of tax

The average rate of tax is total tax paid divided by total income, expressed as a percentage.

Amara: $\frac{2{,}000}{20{,}000} \times 100 = 10\%$

Boas: $\frac{10{,}000}{50{,}000} \times 100 = 20\%$

Part (c): Progressive, proportional or regressive?

A tax is progressive if the average rate of tax rises as income rises, proportional if the average rate stays the same at all income levels, and regressive if the average rate falls as income rises.

Here, Amara (the lower earner, $20,000) pays an average rate of $10\%$ , while Boas (the higher earner, $50,000) pays a higher average rate of $20\%$ . Since the average rate of tax rises as income rises, this tax system is progressive.

Part (d): Transfer payments compared with the tax system

A transfer payment is a payment made by the government directly to an individual for which no good or service is supplied in return, for example, a state retirement pension paid to someone no longer working, or unemployment benefit.

This differs from the income tax system above in the direction in which it redistributes income. The progressive tax redistributes income by taking a larger proportion away from higher earners like Boas (a flow of money from the household to the government). A transfer payment instead redistributes income by directly adding to the income of the recipient (a flow of money from the government to the household), for example, funding a pension for someone with little or no income of their own. Governments typically use both together: taxing higher incomes progressively, then using some of that revenue to fund transfer payments that raise the incomes of the poorest households.

Final answers

(a) Amara’s tax $=$ $2,000; Boas’s tax $=$ $10,000.
(b) Amara’s average tax rate $=$ $10\%$ ; Boas’s average tax rate $=$ $20\%$ .
(c) The system is progressive, since the average rate of tax rises from $10\%$ to $20\%$ as income rises.
(d) A transfer payment (e.g. a pension) adds directly to a recipient’s income, whereas the progressive tax takes a larger share away from higher earners.