1. INCOME REDISTRIBUTION
Chapter 6
©2016 by McGraw-Hill Education Limited.

2. Learning Objectives
Define market income, total income and income after taxes and transfers.
Explain how the Lorenz curve and the Gini coefficient can be used to measure income inequality.
Summarize how the low income ratio and the low income gap ratio can be used to measure poverty in Canada.
Describe the alternative views on redistribution that are embedded in the additive social welfare function and the maximin criteria.

3. Learning Objectives (cont)
Explain how distortionary taxation affects the policy prescriptions for redistribution given an additive social welfare function and the maximin criteria.
Describe what Pareto efficient redistribution is and how it differs rom the additive and maximin social welfare functions.
Summarize the arguments made in favour of pursuing redistribution using in-kind transfers rather than cash transfers.

4. Distribution of Income
LO1, LO2
Distribution of Income
The Lorenz curve
The Gini coefficient
Market income
Income after taxes and transfers
The income share of the richest 1 percent

5. The Lorenz Curve: Income Inequality in Canada, 1980 and 2011
Figure 6.1

6. LO2
The Gini Coefficient for Canada (based on market income and after taxes and transfers), 1980 to 2011
Figure 6.2

7. Income Share of the Top One Percent in Canada (1920-2010) and the United States (1920-2012)*
Figure 6.3

8. LO3
Poverty
Poverty can be defined as lacking sufficient resources to meet current needs
Practically, difficult to define “sufficient” and “needs”
Low income rate
Low income gap ratio
Poverty line

9. Low Income Rates in Canada (in percent)
Figure 6.4

10. Average Low Income Gap Ratio, 1980 and 2011 (in percent)
Table 6.1

11. Interpreting the Data The choice of income measure is important
The choice of income measure is important
Some important sources of income are excluded from the data
In-kind transfers
Payments made in commodities or services
The household unit
Time frame

12. Rationale for Income Distribution Utilitarianism
LO4, LO5
Rationale for Income Distribution Utilitarianism
Utilitarian Social Welfare Function: W = F(U1, U2, …, Un)
Additive Social Welfare Function W = U1 + U2 + … + Un
Assumptions
1. Individuals have identical utility functions that depend only on their incomes
2. Utility functions exhibit diminishing marginal utility of income
3. Total amount of income to society is fixed

13. LO4, LO5
Model of the Optimal Distribution of Income: The Additive Social Welfare Function
Paul’s marginal utility
Peter’s marginal utility e
This is the net gain to society f d c
Social welfare maximized
MUPeter
MUPaul 0’ a b I*
Paul’s income
Peter’s income
Figure 6.5

14. LO4, LO5
The Maximin Criterion
Social Welfare Function W = Minimum(U1, U2, …, Un)
Maximin criterion – maximize the utility of the person with the minimum utility
Original position
Critique of Rawls

15. Alternative Social Welfare Functions and Redistribution
LO4, LO5
Alternative Social Welfare Functions and Redistribution
Panel a: Additive Social Welfare Function
Panel b: Maximin Criterion
Peter’s utility
45o line
Peter’s utility
45o line i K K e i c d S0 C C f S1 W0 W1 C L
Paul’s utility C L
Paul’s utility
Figure 6.6

16. Pareto Efficient Income Redistribution
LO6
Pareto Efficient Income Redistribution
Will redistribution always make someone worse off?
Redistribution if gain in utility from altruism exceeds loss from reduced consumption
Government reduces cost of redistribution
Income distribution as a Public Good
Social stability

17. Non-individualistic Views
Fundamental principles specifying income distribution derived independent of tastes
Plato’s 4:1 ratio of highest to lowest income
Incomes distributed equally as matter of principle

18. Other Considerations Processes versus Outcomes
Fairness of the process by which distribution is determined
Fairness of the procedures used to redistribute it
Robert Nozick
Society cannot redistribute income because society has no income to redistribute
With sufficient social mobility, distribution of income is of no particular ethical interest

19. Cash Versus In-Kind TransfersZ
Y+X K A Y E2 C2 E1 C1 I2
C’2 I1 B Z’ H1 H2 H
Figure 6.7

20. An In-Kind Transfer that Results in a Lower Utility Level than a Cash TransferZ
Y+X E3 A Y K I3 E1 I2 I1 B Z’ H
Figure 6.8

21. Cash and In-Kind Transfers Under Asymmetric InformationUB
UA = CA + H
UB = CB + h ∙ T
R = CA + CB + T a R g b c E1 e
45o d H
R+H UA
Figure 6.9

22. Reasons for In-Kind Transfers
LO7
Reasons for In-Kind Transfers
Commodity egalitarianism
Paternalism
Political motivations

23. Chapter 6 Summary
The Lorenz curve, the Gini coefficient, and the income share of the top 1 percent are indicators of income inequality and are sometimes used to compare income inequality over time, across countries, or before and after government taxes and transfers.
Recent trends indicate that the distribution of income in Canada has become more unequal since 1980.
The low income rate, a measure of poverty, is calculated as the percentage of a given population with income below a certain threshold income level. A measure of the depth of poverty is the average low income gap ratio for a given population.
Measuring income inequality and poverty is difficult because income is hard to measure correctly.

24. Chapter 6 Summary (cont)
If (1) social welfare is the sum of identical utility functions that depend only on income, (2) there is decreasing marginal utility of income, and (3) the total amount of income is fixed, then income should be equally distributed. These are quite strong assumptions, and weakening them gives radically different results.
The maximin criterion states that the best income distribution maximizes the utility of the person who has the lowest utility. The ethical validity of this proposition is controversial.
The income distribution may be like a public good—everyone derives utility from the fact that income is equitably distributed, but government coercion is needed to accomplish redistribution.
The prevalence of government in-kind transfer programs may be due to asymmetric information, paternalism, commodity egalitarianism, or political attractiveness.