Inequality: Study Guide (Microeconomics 6.5)

Why markets can produce unequal outcomes

Topics 6.1 to 6.4 asked whether markets use resources efficiently. This topic asks a different question: who gets the output? A market can be perfectly efficient and still leave some people very rich and others very poor. Efficiency is about the size of the pie; equity is about how it is shared.

Two words are easy to mix up:

• Income is a flow: what a person or household receives over a period, such as wages, rent, interest, profit and government transfers per year.
• Wealth is a stock: the value of everything a household owns (savings, shares, houses, land, businesses) minus its debts, at one moment.

The two are linked. Wealth produces income (rent from a flat, interest on savings), and saved income becomes wealth. In most economies wealth is shared out more unequally than income, because wealth builds up over time and can be passed on.

Measuring inequality

Income levels and poverty rates

The simplest measures compare average income between groups, and the poverty rate:

Poverty rate = people (or households) with income below the poverty line ÷ total population × 100

A poverty line is an income level set by a government or researcher. It may be absolute (enough to buy a fixed basket of essentials) or relative (for example, a set fraction of the typical income).

Income levels and poverty rates differ widely:

• within a country, between groups such as age groups, men and women, racial or ethnic groups, and regions;
• between countries, where average incomes can differ many times over.

So a single national average hides a lot. Two countries with the same average income can have very different poverty rates if one shares income out much more unequally.

The Lorenz curve

A Lorenz curve shows what share of total income (or wealth) goes to each share of the population, after lining everyone up from poorest to richest.

• Horizontal axis: cumulative percentage of households, from poorest to richest.
• Vertical axis: cumulative percentage of income those households receive.
• The 45° line of equality is where every household has the same income: the poorest 20% get 20% of income, the poorest 40% get 40%, and so on.

The farther the Lorenz curve sags below the line of equality, the more unequal the distribution. A curve on the line of equality means perfect equality.

We use two fictional countries. Each point on the table shows the share of income received by the poorest part of the population.

Poorest share of households	20%	40%	60%	80%	100%
Velmora: cumulative share of income	6%	17%	33%	56%	100%
Tarrin: cumulative share of income	9%	23%	41%	64%	100%

The Gini coefficient

The Gini coefficient turns the Lorenz curve into one number. It measures how big the gap is between the Lorenz curve and the line of equality, compared with the whole area under the line of equality.

• Gini = 0: perfect equality (the Lorenz curve is the line of equality).
• Gini = 1: perfect inequality (one household has all the income).
• A higher Gini means more inequality.

Velmora’s Gini coefficient is about 0.35 and Tarrin’s is about 0.25, which matches what the curves show. You will not be asked to draw a Lorenz curve or calculate a Gini coefficient. You will be asked to read the curves and compare distributions across countries, policies or time periods.

Remember what these measures do not show. A Lorenz curve and a Gini coefficient describe shares, not levels. A poor country and a rich country can have the same Gini coefficient.

Worked example 1: reading and comparing Lorenz curves

Question. Use the table and Figure 1. (a) What share of income do the poorest 40% of households receive in each country? (b) What share of income do the richest 20% receive in each country? (c) Velmora introduces cash transfers to low-income households, paid for by a tax on high incomes. Afterwards, the poorest 40% receive 19% of income and the richest 20% receive 41%. Its new Gini coefficient is about 0.31. Describe how Velmora’s Lorenz curve has moved. (d) Can you tell from the curves which country has the higher average income?

(a) Read up from 40% on the horizontal axis. Velmora: 17% of income. Tarrin: 23% of income.

(b) The poorest 80% receive 56% in Velmora, so the richest 20% receive 100 − 56 = 44%. In Tarrin: 100 − 64 = 36%.

(c) The poorest 40% now receive more (19% instead of 17%) and the richest 20% receive less (41% instead of 44%). The Lorenz curve has moved closer to the line of equality, and the Gini coefficient has fallen from about 0.35 to about 0.31. Inequality after taxes and transfers is lower than before.

(d) No. The curves show shares of each country’s total income, not the amounts. Tarrin is more equal, but its households could still be poorer than Velmora’s on average.

Check. In (b) we subtracted the cumulative share at 80% from 100%. Reading 56% as the richest group’s share is a common slip: 56% is what the poorest 80% receive.

Sources of income and wealth inequality

1. Factors are paid the value of their marginal product

From Unit 5, a profit-maximising firm in competitive markets hires a factor until the factor’s price equals its marginal revenue product. When the firm sells in a perfectly competitive market, that is the value of the marginal product:

Value of marginal product = marginal product × price of the output

So each factor of production (labour, capital, land) tends to earn the value of what it adds to output. This is efficient, but it is not equal:

• workers whose skills add more output, or whose output sells for a higher price, earn more;
• owners of capital and land receive income from what their machines and land produce. Households that own more of these assets earn more, which lets them save and own still more.

2. Other sources

Source	How it creates inequality
Tax structure	A progressive tax narrows after-tax income gaps; a regressive tax widens them (see Worked example 3).
Human capital	Education, training, skills and health raise a worker’s marginal product and so their pay. People who cannot afford training fall behind.
Social capital	Networks of contacts, trust and connections help people hear about jobs, get recommendations and start businesses.
Inheritance	Wealth (and the income it earns) passes between generations, so inequality can persist.
Discrimination	Workers may be paid less than the value of their marginal product, or kept out of jobs, schools or loans, because of age, gender, race or other traits.
Access to financial markets	People who can borrow can invest in education, a house or a business. People who cannot borrow, or pay high interest, miss these chances.
Mobility	Being able to move between places, jobs or industries lets people go where their marginal product is valued most. Low mobility traps people in low-paid areas or work.
Bargaining power	Within firms (managers and staff), labour unions (collective bargaining can raise members’ pay) and families (who controls the household’s income), the stronger side takes a bigger share.

Worked example 2: marginal product and pay

Question. Lindqvist Prints, a fictional firm, sells printed banners for $12 each in a perfectly competitive market. Hiring one more skilled technician adds 9 banners per hour. Hiring one more helper adds 3 banners per hour. Renting one more printing machine adds 14 banners per hour. (a) Find the value of the marginal product of each factor. (b) If each is paid the value of its marginal product, how many times more does a technician earn per hour than a helper? (c) The helpers complete a training course that raises their marginal product to 5 banners per hour. Find the new ratio and name the source of inequality involved. (d) Who receives the income from the machine, and how does this link to wealth?

(a)

1. Technician: 9 × $12 = $108 per hour.
2. Helper: 3 × $12 = $36 per hour.
3. Machine: 14 × $12 = $168 per hour.

(b) $108 ÷ $36 = 3. The technician earns three times as much, with no discrimination involved: the gap comes from different marginal products.

(c) Helper’s new value of marginal product = 5 × $12 = $60 per hour. Ratio = $108 ÷ $60 = 1.8. Training raised the helpers’ human capital, which raised their marginal product and narrowed the pay gap.

(d) The owner of the machine receives the $168 per hour it earns, as rental income or profit. Only households that already own capital (wealth) receive this income, and they can save part of it to buy more capital. This is one reason wealth inequality tends to persist and grow.

Check. Units: banners per hour × dollars per banner = dollars per hour.

Worked example 3: progressive and regressive taxes

To classify a tax, compare the average tax rate:

Average tax rate = tax paid ÷ income × 100

Type	Average tax rate as income rises	Effect on after-tax inequality
Progressive	rises	reduces it
Proportional	stays the same	no change in income ratios
Regressive	falls	increases it

Question. Three fictional households: Ash earns $20,000 and spends $19,000; Birch earns $60,000 and spends $45,000; Cedar earns $200,000 and spends $110,000. Tax X is a 10% sales tax on all spending. Tax Y is an income tax of 0% on the first $25,000 of income and 20% on income above $25,000. (a) Find each household’s tax and average tax rate under X and under Y. Classify each tax. (b) Before tax, Cedar’s income is 10 times Ash’s. Find the ratio of after-tax incomes under each tax.

(a)

Household	Tax X	Average rate X	Tax Y	Average rate Y
Ash	10% × $19,000 = $1,900	9.50%	$0	0%
Birch	10% × $45,000 = $4,500	7.50%	20% × $35,000 = $7,000	11.67%
Cedar	10% × $110,000 = $11,000	5.50%	20% × $175,000 = $35,000	17.50%

Under X the average rate falls as income rises, so X is regressive, even though Cedar pays the most dollars. Richer households spend a smaller part of their income. Under Y the average rate rises, so Y is progressive.

(b)

• Tax X: ($200,000 − $11,000) ÷ ($20,000 − $1,900) = $189,000 ÷ $18,100 = 10.44. The gap widens.
• Tax Y: ($200,000 − $35,000) ÷ $20,000 = $165,000 ÷ $20,000 = 8.25. The gap narrows.

Interpretation. A proportional income tax (say 10% for everyone) would leave the ratio at exactly 10. Choosing between tax structures is partly a choice about how much inequality a society accepts.

Common misconceptions

• “Income and wealth are the same thing.” Income is a flow per period; wealth is a stock at a moment. A retired person can have high wealth and low income.
• “A Lorenz curve closer to the axes means more equality.” Equality is the 45° line. The farther the curve bows away from it, towards the bottom-right corner, the more unequal the distribution.
• “A higher Gini coefficient means a richer country.” The Gini coefficient measures how income is shared, not how much there is.
• “A tax that takes more dollars from the rich is progressive.” Use the average tax rate (percentage of income). A sales tax takes more dollars from the rich but is usually regressive.
• “All pay differences come from discrimination.” Differences in marginal product, human capital and bargaining power also cause pay gaps. Discrimination is one source among several.
• “If markets are efficient, the outcome is fair.” Efficiency and equity are different goals. An efficient market can still give very unequal incomes.
• “A rise in inequality means the poor got poorer.” A Lorenz curve shows shares. The poorest group’s share can fall while its income still rises, if total income grows faster.

Where this leads

This is the last topic of the course. It links back to factor markets (Unit 5), where you met marginal revenue product, and to the previous topic, the effects of government intervention, where taxes and transfers change market outcomes. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate, and finish with a review of the whole course roadmap.