These are original Marlbridge practice questions, not past exam questions. The mark points are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. All countries, firms, people and data are fictional. Only basic arithmetic (add, subtract, multiply, divide) is needed, so a four-function calculator is enough. You are not asked to draw a Lorenz curve or calculate a Gini coefficient; those are outside the course.
Question 1 uses points on the Lorenz curves of two fictional countries, Pellam and Rudd:
| Poorest share of households | 20% | 40% | 60% | 80% | 100% |
|---|---|---|---|---|---|
| Pellam: cumulative share of income | 5% | 14% | 29% | 52% | 100% |
| Rudd: cumulative share of income | 8% | 20% | 37% | 60% | 100% |
Question 1 (multiple choice · foundation)
Which statement is supported by the table?
- (A) The richest 20% of households receive 48% of income in Pellam and 40% in Rudd.
- (B) Pellam’s Lorenz curve lies closer to the line of equality than Rudd’s.
- (C) The poorest 20% of households in Rudd receive 20% of income.
- (D) Average household income is lower in Pellam than in Rudd.
Answer and explanation
Answer: (A). The poorest 80% receive 52% in Pellam, so the richest 20% receive 100 − 52 = 48%. In Rudd, 100 − 60 = 40%.
- (B) reverses the rule. Pellam’s shares are lower at every point, so its curve sags farther from the line of equality: Pellam is more unequal.
- (C) reads the wrong column. 20% is what Rudd’s poorest 40% receive; the poorest 20% receive 8%.
- (D) confuses shares with levels. A Lorenz curve shows how income is divided, not how much there is.
Question 2 (multiple choice · core)
Households in a fictional country earn $10,000, $40,000 and $100,000 a year. Which tax schedule is regressive?
- (A) Taxes of $1,000, $4,000 and $10,000
- (B) Taxes of $1,500, $4,000 and $7,000
- (C) Taxes of $500, $4,000 and $15,000
- (D) Taxes of $0, $3,000 and $12,000
Answer and explanation
Answer: (B). Average tax rates are 1,500 ÷ 10,000 = 15%, 4,000 ÷ 40,000 = 10% and 7,000 ÷ 100,000 = 7%. The rate falls as income rises, so the tax is regressive, even though richer households pay more dollars.
- (A) gives 10%, 10%, 10%: a constant rate, so it is proportional.
- (C) gives 5%, 10%, 15%: a rising rate, so it is progressive.
- (D) gives 0%, 7.5%, 12%: also rising, so progressive.
Question 3 (multiple choice · core)
Over ten years, a fictional country’s Gini coefficient for income rises from 0.31 to 0.38. Which statement must be true?
- (A) Income became more unequally distributed, and the gap between the Lorenz curve and the line of equality grew.
- (B) Average income in the country fell.
- (C) The poverty rate rose.
- (D) Households in the poorest 20% received fewer dollars of income than ten years earlier.
Answer and explanation
Answer: (A). A higher Gini coefficient means a larger gap between the Lorenz curve and the line of equality, which is greater inequality.
- (B) confuses distribution with level. The Gini coefficient says nothing about average income, which may have risen.
- (C) is possible but not certain. The poverty rate depends on how many people are below a poverty line, which also depends on income levels.
- (D) confuses shares with amounts. The poorest group’s share could fall while its income in dollars rises, if total income grew.
Question 4 (multiple choice · foundation)
Teodor and Mira graduate from the same course with the same grades. Teodor is offered an interview for a well-paid job after a family friend who works at the firm recommends him. Mira does not hear about the job. Which source of inequality does this illustrate?
- (A) Human capital
- (B) Social capital
- (C) Inheritance
- (D) A regressive tax structure
Answer and explanation
Answer: (B). Social capital is the value of a person’s networks and connections. Teodor’s contact gives him access to a job that Mira, with the same skills, does not reach.
- (A) is wrong because their education and grades, which make up human capital, are the same.
- (C) is wrong because nothing is passed down as wealth; the advantage is a contact, not an asset.
- (D) is wrong because no tax is involved.
Question 5 (calculation and explanation · core)
Pomeroy Juices, a fictional firm, sells juice boxes for $2 each in a perfectly competitive market. One more machine technician adds 40 boxes per hour. One more line packer adds 9 boxes per hour. One more bottling machine, owned by an investor, adds 60 boxes per hour. Assume each factor is paid the value of its marginal product.
(a) Calculate the hourly pay of a technician and of a packer, and the ratio between them. (b) The packers complete a training programme that raises their marginal product to 15 boxes per hour. Calculate the new pay ratio and name the source of inequality this shows. (c) Calculate the hourly income the investor receives from the machine, and explain how this can increase wealth inequality over time.
Model answer and suggested Marlbridge rubric
(a) Technician: 40 × $2 = $80 per hour. Packer: 9 × $2 = $18 per hour. Ratio: 80 ÷ 18 = 4.44.
(b) Packer’s new pay: 15 × $2 = $30 per hour. New ratio: 80 ÷ 30 = 2.67. The gap narrows because training raised the packers’ human capital, and so their marginal product.
(c) 60 × $2 = $120 per hour, paid to the machine’s owner. Only people who already own capital receive this income. They can save part of it and buy more capital, which earns still more income, so the gap between owners and non-owners of wealth can grow over time.
| Point | What earns it |
|---|---|
| 1 | $80 and $18 per hour, with the ratio 4.44 |
| 1 | $30 per hour and ratio 2.67 |
| 1 | Human capital named and linked to a higher marginal product |
| 1 | $120 per hour and the link from owning capital to income to more wealth |
Common error: using the number of boxes, not their value. Pay is marginal product times the output price.
Question 6 (calculation and explanation · core)
Brenmark, a fictional country, has an income tax of 0% on the first $15,000 of income, 10% on income from $15,000 to $50,000, and 30% on income above $50,000. Three households earn $12,000, $40,000 and $120,000.
(a) Calculate the tax paid and the average tax rate for each household. Classify the tax. (b) Before tax, the richest household earns 10 times as much as the poorest. Calculate the ratio of after-tax incomes. (c) Brenmark replaces the income tax with a lump-sum tax of $3,000 per household. Calculate each household’s average tax rate, classify the new tax and find the new after-tax income ratio. (d) Explain why the choice of tax structure is a source of income inequality.
Model answer and suggested Marlbridge rubric
(a)
| Income | Tax | Average tax rate |
|---|---|---|
| $12,000 | $0 | 0% |
| $40,000 | 10% × $25,000 = $2,500 | 6.25% |
| $120,000 | 10% × $35,000 + 30% × $70,000 = $3,500 + $21,000 = $24,500 | 20.42% |
The average rate rises with income, so the tax is progressive.
(b) ($120,000 − $24,500) ÷ $12,000 = $95,500 ÷ $12,000 = 7.96. The gap narrows from 10 to 7.96.
(c) Average rates: 3,000 ÷ 12,000 = 25%, 3,000 ÷ 40,000 = 7.5%, 3,000 ÷ 120,000 = 2.5%. The rate falls as income rises, so the tax is regressive. After-tax ratio: $117,000 ÷ $9,000 = 13. The gap widens from 10 to 13.
(d) Taxes take different shares of different incomes. A progressive tax takes a larger share from high incomes and narrows after-tax gaps; a regressive tax takes a larger share from low incomes and widens them. So two countries with the same before-tax incomes can have different after-tax inequality.
| Point | What earns it |
|---|---|
| 1 | All three taxes correct and classified as progressive using the average rates |
| 1 | After-tax ratio 7.96 |
| 1 | Lump-sum rates 25%, 7.5%, 2.5%, classified as regressive, ratio 13 |
| 1 | Explanation links the average tax rate pattern to wider or narrower after-tax gaps |
Common error: applying 30% to the whole $120,000. Each rate applies only to the income inside its band. Accept a correct answer to (d) that refers to a proportional tax leaving the ratio unchanged.
Question 7 (explanation · stretch)
Ossery is a fictional region with a poverty line of $14,000 per person per year. Of 4,000 people aged 18 to 24, 920 have incomes below the poverty line. Of 12,000 people aged 25 to 64, 1,080 do.
(a) Calculate the poverty rate for each age group and for the two groups combined. (b) Using two different sources of inequality from this topic, explain why young adults in Ossery might have lower incomes than older adults. (c) Explain why wealth in Ossery is likely to be distributed more unequally than income. Refer to inheritance and to access to financial markets. (d) A new rail line lets workers from Ossery commute to a city where pay is higher. Explain how this could reduce inequality.
Model answer and suggested Marlbridge rubric
(a) Ages 18 to 24: 920 ÷ 4,000 × 100 = 23%. Ages 25 to 64: 1,080 ÷ 12,000 × 100 = 9%. Combined: 2,000 ÷ 16,000 × 100 = 12.5%. The overall rate hides a large gap between the groups.
(b) Any two, each with a reason:
- Human capital: young adults have less work experience and fewer job-specific skills, so their marginal product, and pay, is lower.
- Bargaining power: new workers are less able to negotiate pay within firms, and may be less likely to be covered by a union agreement.
- Social capital: they have built fewer professional contacts, so they hear about fewer well-paid jobs.
- Access to financial markets: with no credit history they may struggle to borrow for training or to start a business.
(c) Wealth builds up over a lifetime and can be inherited, so some families start with large assets while others start with none. People with wealth or good credit have better access to financial markets: they can borrow to buy houses, shares or businesses, which earn income and grow in value. People without access cannot do this. So wealth gaps add up across years and generations, while income is earned fresh each year.
(d) The rail line raises mobility. Workers can reach jobs where their marginal product is valued more highly, so low-income workers in Ossery can earn more. This narrows the income gap between Ossery and the city, and within Ossery between those who already had well-paid local jobs and those who did not.
| Point | What earns it |
|---|---|
| 1 | Poverty rates 23%, 9% and 12.5% |
| 1 | First source correctly named and explained for young adults |
| 1 | Second, different source correctly named and explained |
| 1 | Inheritance and access to financial markets linked to wealth accumulating over time |
| 1 | Mobility linked to higher pay for low-income workers and a narrower gap |
Do not award (b) points for “discrimination” unless the answer explains how it applies to age.
How did you do?
- Q1 or Q3 wrong: re-read “The Lorenz curve”, “The Gini coefficient” and Worked example 1 in the study guide. Remember: shares, not levels.
- Q2 or Q6 wrong: re-read Worked example 3. Always compare average tax rates.
- Q5 wrong: re-read “Factors are paid the value of their marginal product” and Worked example 2.
- Q4 or Q7 incomplete: re-read the table of sources and make sure each explanation names the source and says how it changes income or wealth.
Then tick off the topic checklist.