Bellara's government levies income tax according to the following schedule of marginal tax rates. Each rate applies only to the portion of a person's income that falls within that band. Band of taxable income Marginal tax rate $0 – $20,000 10% $20,001 – $50,000 20% Above $50,000…

Answer: ((a)) Aiden's tax is 0.10×20000 + 0.20×20000 = 2000+4000 = 6000, i.e. $6,000, so Aiden's average rate of tax is 6000/40000×100=15% ((b)) Priya's tax is 0.10×20000+0.20×30000+0.30×30000=2000+6000+9000=17000, i.e. $17,000, so Priya's average rate of tax is 17000/80000×100=21.25%, and the marginal rate of tax on Priya's last dollar earned is 30% ((c)) Since the average rate of tax rises from 15% at the lower income to 21.25% at the higher income, Bellara's income tax schedule is progressive ((d)) A progressive tax follows the ability-to-pay principle, taking a larger proportion of income from those with a greater capacity to pay, which is often seen as a fairer way to share the burden of financing government spending than a proportional tax that takes the same proportion…. Part (a): Aiden's tax and average rate of tax Aiden's taxable income of $40,000 spans the first two tax bands: the first $20,000 is taxed at 10%, and the remaining 40000-20000=20000 dollars falls in the second band and is taxed at 20%. Tax…

AS Level Economics 9708: Progressive Tax, Average and Marginal Tax Rates

Band of taxable income	Marginal tax rate
$0 – $20,000	10%
$20,001 – $50,000	20%
Above $50,000	30%

Band of taxable income

Marginal tax rate

$0 – $20,000

10%

$20,001 – $50,000

20%

Above $50,000

30%

Part (a): Aiden’s tax and average rate of tax

Aiden’s taxable income of $40,000 spans the first two tax bands: the first $20,000 is taxed at $10\%$ , and the remaining $40000-20000=20000$ dollars falls in the second band and is taxed at $20\%$ .

$\text{Tax} = (0.10\times20000) + (0.20\times20000) = 2000+4000 = 6000$

So Aiden pays $6,000 in tax. Aiden’s average rate of tax (ART) is total tax divided by total income:

$ART = \frac{6000}{40000}\times100 = 15\%$

Part (b): Priya’s tax, average rate of tax and marginal rate of tax

Priya’s taxable income of $80,000 spans all three bands: $20,000 at $10\%$ , the next $30,000 (from $20,001 to $50,000) at $20\%$ , and the remaining $80000-50000=30000$ dollars at $30\%$ .

$\text{Tax} = (0.10\times20000)+(0.20\times30000)+(0.30\times30000) = 2000+6000+9000 = 17000$

So Priya pays $17,000 in tax, and her average rate of tax is:

$ART = \frac{17000}{80000}\times100 = 21.25\%$

Since Priya’s income falls in the top band, the marginal rate of tax (MRT) on the very last dollar she earns is $30\%$ . The rate that applies to that band.

Part (c): Progressive, proportional or regressive?

Comparing the two average rates of tax: Aiden’s ART is $15\%$ on an income of $40,000, while Priya’s ART is $21.25\%$ on a higher income of $80,000. Because the average rate of tax rises as income rises, Bellara’s income tax schedule is progressive. (A proportional tax would leave ART unchanged as income rises, and a regressive tax would see ART fall as income rises.)

Part (d): Why choose a progressive tax over a proportional tax?

One reason is the ability-to-pay principle: a progressive tax deliberately takes a larger proportion of income from people with higher incomes, on the grounds that they have a greater capacity to bear the burden of tax without a large loss of wellbeing, compared with someone on a lower income. This is often regarded as a fairer basis for raising the revenue a government needs for its spending than a proportional tax, which takes the same proportion of income from every taxpayer regardless of how easily they can afford it.

Final answers

(a) Aiden’s tax $=$ $6,000; ART $=$ 15%
(b) Priya’s tax $=$ $17,000; ART $=$ 21.25%; MRT on last dollar $=$ 30%
(c) The tax schedule is progressive, since ART rises from 15% to 21.25% as income rises
(d) The ability-to-pay principle. Progressive tax takes a larger share from those more able to afford it