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9708 · 8.2

Equity and redistribution of income and wealth — practice questions

Practice and worked examples for 9708 Equity and redistribution of income and wealth. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

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.

Worked example 2

An economist is analysing the progressive tax system in a country. An individual earns a gross annual income of $80,000. The income tax bands are as follows:

  • Personal Allowance (0% tax): 0−0 - 15,000
  • Basic Rate (20% tax): 15,001−15,001 - 50,000
  • Higher Rate (40% tax): Above 50,00050,000

Calculate: a) The total income tax paid by the individual. b) The individual's disposable income. c) The individual's average rate of tax.

Show solution outline

Step 1: Calculate tax for each band

  • Personal Allowance band: The first $15,000 is taxed at 0%. Tax = 15,000∗0.00=15,000 * 0.00 = 0
  • Basic Rate band: Income between $15,001 and $50,000. The amount of income in this band is 50,000−50,000 - 15,000 = 35,000.35,000. Tax = 35,000∗0.20=35,000 * 0.20 = 7,000
  • Higher Rate band: Income above $50,000. The amount of income in this band is $80,000 - 50,000=50,000 = 30,000. Tax = 30,000∗0.40=30,000 * 0.40 = 12,000

Step 2: Calculate total income tax paid (a) Total Tax = Tax from all bands Total Tax = 0+0 + 7,000 + 12,000=12,000 = 19,000

Step 3: Calculate disposable income (b) Disposable Income = Gross Income - Total Tax Disposable Income = 80,000−80,000 - 19,000 = 61,00061,000

Step 4: Calculate the average rate of tax (c) Average Tax Rate = (Total Tax / Gross Income) * 100 Average Tax Rate = (19,000/19,000 / 80,000) * 100 = 23.75%

Conclusion: The individual pays a total of $19,000 in income tax, resulting in a disposable income of $61,000. Their average tax rate is 23.75%, which is lower than their marginal tax rate of 40%, demonstrating the nature of a progressive system.

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