Questions & explanations
1. What trade-offs exist between actuarial fairness and social insurance objectives?
Actuarial fairness rewards prudent behavior (e.g., safe driving) but can exclude high-risk people who cannot afford high premiums. Social insurance guarantees coverage for all, but it may distort incentives: people might take more risks if insurance does not charge them accordingly. For example, if health insurance premiums are not based on lifestyle, people might smoke more. Also, social insurance usually requires mandatory participation, which some view as limiting freedom. But the trade-off is that it achieves universal coverage and solidarity. The balance depends on society's values: more actuarial fairness means less redistribution, while more social insurance means less individual pricing. Most countries mix both: private health insurance with community rating (similar to social) and public pensions with progressive benefits.
2. Explain how moral hazard relates to the difference between actuarially fair insurance and social insurance.
Moral hazard means people change their behavior when insured, increasing the risk of loss. For example, someone with full health insurance might visit the doctor more often. In actuarially fair private insurance, insurers try to reduce moral hazard through co-pays or deductibles, so the insured still bears some cost. In social insurance, co-pays are often lower or absent, so moral hazard can be larger. However, social insurance may accept this because the goal is access and redistribution, not minimizing cost. Also, social insurance sometimes uses non-price mechanisms like waiting times or gatekeeping to control use. The key is that actuarial fairness emphasizes efficiency and risk pricing, while social insurance emphasizes equity and access, even at the cost of some efficiency loss from moral hazard.
3. Explain the difference between the Lorenz curve for wealth versus income and why the Gini for wealth is usually higher.
A Lorenz curve for wealth plots the share of total wealth owned by the poorest x% of people. Wealth includes assets like houses, stocks, and savings, minus debts. Income is the flow of money earned over time. Wealth is typically much more concentrated than income because rich people save and invest, accumulating assets that grow. The Lorenz curve for wealth bows much further from the diagonal, so the wealth Gini is often 0.7–0.9 in many countries, while income Gini is 0.3–0.6. For example, the top 10% might own 70% of wealth but earn only 40% of income. The wealth curve also can have negative values for people with negative net worth (more debt than assets), which is impossible for income. This difference matters for policy: taxing wealth is different from taxing income.
4. How does social insurance differ from actuarially fair private insurance?
Social insurance, like public pensions or unemployment benefits, is run by the government and often not actuarially fair. Premiums (or taxes) are usually based on income, not individual risk. So low-risk people may pay more than their expected benefits, and high-risk people pay less. This creates redistribution: from rich to poor, or from healthy to sick. Private insurance, if actuarially fair, charges each person their own risk, so no redistribution across groups. Social insurance also aims to cover everyone (not just those who can afford it) and often includes a social solidarity component. For example, in Social Security, high earners pay more in payroll taxes but may get only slightly higher benefits, transferring money to lower earners.
5. How does the Samuelson condition differ from the condition for a private good?
For a private good, we compare just one person's marginal benefit to the marginal cost because the good is used by one person. For example, a pizza eaten by one person: if that person's extra happiness from an extra slice is $2 and the slice costs $1, buy it. But for a public good, we add all people's marginal benefits. So the condition is: sum of marginal benefits = marginal cost, versus for private goods: each person's marginal benefit = marginal cost separately. Also, for private goods, the market naturally leads to this condition because people buy until their own benefit equals price. For public goods, the market fails without collective action. So the Samuelson condition highlights the need for government or group decisions.
6. What is the Kuznets curve hypothesis?
The Kuznets curve hypothesis, proposed by Simon Kuznets in the 1950s, says that inequality first rises and then falls as a country develops economically. It looks like an upside-down U on a graph with economic development on the horizontal axis and inequality on the vertical axis. In early stages, workers move from low-inequality agriculture to higher-inequality industry, so inequality grows. Later, as more people benefit from education and social programs, inequality declines. Kuznets used data from the US, UK, and Germany up to the 1950s to support this pattern. However, the hypothesis is debated today because many countries have not seen a clear decline. It remains a starting point for thinking about development and inequality.
7. What are the main criticisms of the Kuznets curve hypothesis today?
Key criticisms are that the curve does not always hold. Many developing countries today have stayed unequal without the predicted decline. Data for early industrializers like the US may be flawed because they excluded top incomes. Also, Kuznets ignored the role of institutions and policies: countries that invest in education and progressive taxes see inequality fall, but those that do not can remain unequal. The hypothesis is too simple—it assumes development automatically leads to equality, but politics and global forces matter. Some economists say the curve is not a law but a description of one historical period. Furthermore, rising inequality in rich nations since 1980 directly contradicts the downward part of the curve.
8. Describe how you can decompose the Gini coefficient by income sources like wages and capital income.
The Gini coefficient can be broken down to show how much each source of income contributes to overall inequality. Each source has its own share of total income and its own concentration (how unequally that source is distributed). The decomposition formula is: total Gini = sum over sources of (share of source times concentration index of that source). The concentration index is like a Gini but ranks people by total income, not by income from that source. For example, if wage income is 70% of total and has a concentration of 0.3, while capital income is 30% with a concentration of 0.8, then total Gini = 0.7*0.3 + 0.3*0.8 = 0.21+0.24=0.45. This tells us capital income adds more to inequality than its share suggests.
9. Compare the fairness of PAYG and funded systems for low-income workers.
PAYG systems often have a progressive formula: low-income workers get a higher percentage of their pre-retirement earnings compared to high-income workers. This helps reduce poverty in old age. Funded systems, like defined-contribution plans, pay exactly what you saved plus returns. Low-income workers save less because they earn less, so their pensions are small. They may also lack financial knowledge to invest wisely. On the other hand, a funded system can be fairer across generations because each generation pays for its own retirement, not for the previous generation. But without extra help, the poor may end up with very low pensions in a pure funded system. Many countries combine both to balance fairness.
10. Why does Kuznets argue inequality first increases during early industrialization?
Kuznets argued that early industrialization creates a two-sector economy. Most people work in traditional agriculture with low and equal incomes. A small share moves to modern industry where wages are higher but also more unequal. As the industrial sector grows, the average income rises, but the gap between the rich industrial workers and the poor farmers widens. Also, savings are concentrated in the hands of the industrial owners, who reinvest and get richer. So overall inequality increases. This continues until the industrial sector becomes so large that the rural population shrinks, and political pressure leads to redistribution, like public education and progressive taxes, which later reduce inequality.
11. Explain why the Piketty-Saez series are important for the debate about inequality and what they reveal about the '1%'.
These series provide the most reliable long-run evidence that the share of the very richest has surged in recent decades, especially in Anglo-Saxon countries. This undermines the Kuznets idea that inequality automatically falls with development. They show that the top 1% captures a growing fraction of total income, which sparks debates about fairness, democracy, and economic opportunity. The data also show that within the top 1%, the top 0.1% and 0.01% have grown even faster, suggesting extreme concentration. Policy implications include arguing for higher top tax rates, stronger estate taxes, and better data on wealth. The series are a key reason why the '1%' became a symbol of rising inequality.
12. What do the Piketty-Saez top income share series measure?
The Piketty-Saez top income share series measure the share of total national income (or earnings) that goes to the highest-income individuals, like the top 10%, top 1%, or top 0.1%. They use data from income tax returns, which are more reliable for the rich than surveys. The series go back to the early 1900s for some countries, especially the US. They show that in many rich countries, top income shares fell from the 1920s to the 1970s (the 'Great Compression'), then rose sharply after 1980. For example, the top 1% share in the US was about 20% in 1928, fell to below 10% in the 1970s, and climbed back to over 20% by 2010. These series are a key source for understanding long-run inequality trends.