Chapter 13 — Exercises

Section A — Measuring inequality

A1. Suppose an economy has five people with incomes: $10,000, $20,000, $30,000, $50,000, and $90,000. - (a) Compute the total income and each person's share of total income. - (b) Construct the Lorenz curve (plot cumulative population share vs. cumulative income share). - (c) Estimate the Gini coefficient visually from your Lorenz curve.

A2. Now suppose the same economy redistributes so incomes become: $25,000, $30,000, $35,000, $45,000, $65,000. Redo the Lorenz curve. How did the Gini change?

A3. The U.S. income Gini is about 0.39 and the wealth Gini is about 0.85. Why is wealth inequality so much larger? Give three specific reasons.

A4. Look up the Gini coefficient for three countries of your choice (the World Bank's data portal has them). How do they compare to the U.S.? What do you think explains the differences?

Section B — Causes of rising inequality

B1. For each of the four explanations (SBTC, globalization, institutional change, winner-take-all), give one piece of evidence supporting it and one piece of evidence against (or qualifying) it.

B2. "The college wage premium has doubled since 1980." What does this mean, concretely? If a high school graduate earned $35,000 in 1980 and a college graduate earned $45,000, and the premium has doubled, what would the college graduate earn now (holding the high school wage constant)?

B3. CEO-to-worker pay ratios have risen from about 20:1 in 1965 to about 300:1 today. Is this best explained by SBTC, winner-take-all dynamics, institutional change, or some combination?

B4. "If we just strengthen unions, inequality will fall back to 1960s levels." Evaluate using the four-explanation framework. Is institutional change enough, or are other forces at work?

B5. Apply Piketty's r > g framework. If r = 5% and g = 2%, what happens to the wealth share of the top 1% over a generation (roughly 30 years)? (Assume the top 1% saves all of their capital income; this is a simplification.)

Section C — Philosophical frameworks

C1. A policy would raise GDP by 2% but increase the income of the top 10% by 5% and leave the bottom 50% unchanged. Evaluate this policy from: - (a) A utilitarian perspective - (b) A Rawlsian perspective - (c) A libertarian perspective

C2. A policy would reduce GDP by 1% but raise the income of the bottom 20% by 10%. Same three evaluations.

C3. "Bill Gates earned his fortune through voluntary transactions — millions of people chose to buy Windows. Therefore his wealth is just." Evaluate this from each of the three frameworks.

C4. "Nobody deserves to be poor in a rich country." Which framework is this most consistent with? What would each framework say about it?

C5. Pick a real inequality-related policy debate (universal basic income, estate tax, free college, wealth tax). Frame the debate using all three frameworks. Where do the frameworks agree? Where do they diverge?

Section D — Anti-poverty policies

D1. Compare cash transfers to the EITC on three dimensions: cost, work incentive effects, and targeting. Which is better for which purpose?

D2. The expanded Child Tax Credit in 2021 reduced child poverty by roughly 30%. It cost about $100 billion per year. Compute the cost per child lifted out of poverty (use rough numbers). Is this a good value?

D3. "The minimum wage is a bad anti-poverty tool because it doesn't help people who aren't working." Evaluate. What would a comprehensive anti-poverty strategy look like?

D4. Education is often called "the great equalizer." Under what conditions is this true? Under what conditions is it not? (Hint: think about unequal access to quality education, student debt, and the variance of returns.)

D5. Design an anti-poverty package for the United States using all four tools. How much would you spend on each? How would you fund it? What tradeoffs are you accepting?

Section E — The MSU adjunct case

E1. Why does an adjunct professor with a PhD earn less than half of what a tenure-track professor earns? Use the four explanations from §13.2 (adapted to the academic labor market).

E2. Would raising the minimum wage help adjunct professors? Why or why not?

E3. Would unionization of adjunct faculty help? What does the institutional-change explanation predict?

E4. Apply the three philosophical frameworks to the adjunct-tenure gap. Is it just? Unjust? Depends on the framework?

Section F — Data lookup

F1. Look up the U.S. income share of the top 1% on the World Inequality Database (wid.world). What was the share in 1980? In 2000? In 2020?

F2. Look up the U.S. Gini coefficient on the Census Bureau's website or FRED. Plot the trend since 1970.

F3. Look up intergenerational mobility data from Raj Chetty's Opportunity Insights project (opportunityinsights.org). Find the mobility rates for your home county or a county of interest. How does it compare to the national average?

F4. Look up the college wage premium over time (BLS or Census data). When did it start rising? Has it continued to rise in the 2010s and 2020s?

Section G — Policy debate

G1. "We should impose a wealth tax of 2% on assets above $50 million." Evaluate using both economic analysis (efficiency, behavioral responses, revenue estimates) and philosophical frameworks (utilitarian, Rawlsian, libertarian).

G2. "Universal basic income is the simplest and most effective anti-poverty policy." Make the strongest case for and against.

G3. "Inequality is not a problem if everyone's standard of living is rising." Evaluate. Does the evidence support the claim that everyone's standard of living has been rising?

G4. "Inequality is mostly caused by individual differences in talent and effort." Evaluate using the four explanations from §13.2.

Section H — Reflection

  • Which of the three philosophical frameworks is closest to your own intuition about inequality? Has reading this chapter changed your view?
  • The chapter argues that the causes of rising inequality are "genuinely contested." Does this frustrate you, or does it make you more confident that the topic is being taken seriously?
  • After reading this chapter, what is one thing you would change about how the U.S. addresses inequality?

Selected answers in appendices/answers-to-selected.md.