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2281 · 5.2

Poverty — practice questions

Practice and worked examples for 2281 Poverty. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A country's income tax system has the following bands:

  • Personal Allowance (0% tax): up to 10,00010,000
  • Basic Rate (20% tax): 10,001to10,001 to 50,000
  • Higher Rate (40% tax): above 50,00050,000

Calculate the total tax paid and the average tax rate for an individual earning (a) $40,000 and (b) $80,000. Explain why this system is progressive.

Show solution outline

**(a) Individual earning 40,000∗∗40,000**

  1. Tax on first $10,000: This falls within the Personal Allowance.
    • Tax = 10,000×0%=10,000 \times 0\% = 0
  2. Tax on income from 10,001to10,001 to 40,000: The amount in this band is 30,000(30,000 (40,000 - $10,000). This is taxed at the Basic Rate.
    • Tax = 30,000×20%=30,000 \times 20\% = 6,000
  3. Total Tax Paid:
    • Total Tax = 0+0 + 6,000 = 6,0006,000
  4. Average Tax Rate: This is the total tax as a percentage of total income.
    • Average Rate = 600040000×100%=0.15×100%=15%\frac{6000}{40000} \times 100\% = 0.15 \times 100\% = 15\%

** (b) Individual earning 80,000∗∗80,000**

  1. **Tax on first 10,000:∗∗10,000:**
    • Tax = 10,000×0%=10,000 \times 0\% = 0
  2. Tax on income from 10,001to10,001 to 50,000: The full amount in this band is 40,000(40,000 (50,000 - $10,000). This is taxed at the Basic Rate.
    • Tax = 40,000×20%=40,000 \times 20\% = 8,000
  3. Tax on income above $50,000: The amount in this band is $30,000 (80,000−80,000 - 50,000). This is taxed at the Higher Rate.
    • Tax = 30,000×40%=30,000 \times 40\% = 12,000
  4. Total Tax Paid:
    • Total Tax = 0+0 + 8,000 + 12,000=12,000 = 20,000
  5. Average Tax Rate:
    • Average Rate = 2000080000×100%=0.25×100%=25%\frac{20000}{80000} \times 100\% = 0.25 \times 100\% = 25\%

Conclusion on Progressivity: The tax system is progressive because the average tax rate increases as income increases. The individual earning $40,000 pays an average rate of 15%, while the individual earning $80,000 pays a higher average rate of 25%. This demonstrates the principle of vertical equity.

Worked example 2

Country X has a Gini coefficient of 0.42. The government proposes raising the top income tax rate from 40% to 50% and increasing unemployment benefits.

Analyse the likely effects on equity and efficiency. [10 marks]

Show solution outline

Equity effects:

  • Progressive tax rise increases vertical equity — high earners contribute a larger share, narrowing post-tax income gap.
  • Higher benefits raise disposable income for unemployed/low-income households — reduces poverty and likely lowers Gini.

Efficiency / incentive effects:

  • Top earners may reduce labour supply or relocate (tax avoidance) — efficiency loss and possible Laffer curve concern if revenue falls.
  • Higher benefits may reduce job-search intensity (unemployment trap) — structural unemployment risk.
  • Deadweight loss from higher marginal tax rates on middle/high earners.

Judgement: Short-run equity gains are likely; long-run effectiveness depends on behavioural responses and whether revenue funds productive spending (education, health) that raises human capital — potentially improving both equity and efficiency over time.

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