Econ 11, Foldvary

Chapter 20, Income Inequality and Poverty

Mankiw, p. 430: The invisible hand of the marketplace acts to allocate resources efficiently,
but it does not necessarily ensure that resources are allocated fairly.

But what is "fair". What is the fair ownership of labor, capital goods, and land?

Mankiw also says, "When the government enacts policies to make the distribution of income more equitable, it distorts incentives, alters behavior, and makes the allocation of resources less efficient." Is that necessarily so?


How to measure inequality?

A simplistic way to measure inequality is the size distribution:
Divide the population into fifths (table 1, p. 430).
Count the percentage of the income of people in each fifth.

In 2000, the poorest 20% in US got 4.3% of income (table 2, p. 431).
The richest 20% in US got over 47.4%.

Table 2 also shows how the distribution has changed over time.

After 35 the US distribution of income moved towards equality, but since 1970 it has become more unequal again (p. 431).

Part of the reason is that human capital has become more important.

Also, more wealthy and middle-class women are working, raising their income differential relative to poor folk, whose women were already working.

Increasing inequality also shows that ever increasing redistribution and anti-poverty programs have failed to equalize income. The reason is that people change their behavior in response to incentives. If we reward poverty, we get more poverty.

If we tax wealth, people shift their activity to have less of it taxed.

Anti-poverty programs have only treated effects rather than eliminate the causes.

To really measure the extent of inequality, we need to take account of the entire distribution, not just one part of it.

One widely-known way to depict inequality is the Lorenz curve.

Illustrates the entire distribution. Named after Conrad Lorenz, American statistician; 1905.

The Lorenz Curve is a square with a diagonal drawn from the bottom left to the top right.
The horizontal axis measures the cumulative percentage of population, with zero at the left
and 100% at the right corner of the square, from the poorest (on the left) to the richest.

For example, the point 3/4 of the way from the left indicates the lowest 75% of the population.

The vertical axis plots the phenomenon being measured, such as income or wealth,
with zero at the bottom and 100% at the top.

If the distribution has complete equality, the Lorenz curve coincides with the diagonal line.

The more unequal the distribution, the closer the curve to the bottom and right sides of the square. A totally unequal distribution would have one person owning everything and the rest nothing, which would be a curve along the bottom and right sides of the square.

We can also calculate a number based on the Lorenz curve:
the area between the curve and diagonal, divided by triangle.

Called the Gini coefficient, named after Italian statistician, 1912.

zero: perfect equality. 1: complete inequality.

If expressed in percentages, the Gini range is 0 to 100, but I think fractions are clearer.

The Gini coefficient (G) can also be measured directly from the distribution:
G = 1+1/n - (2/[n*n*Y])(y1 + 2y2 + 3y3 + ... nyn),

where y1, y2, ... , yn represent shares in decreasing order of size, and Y is the average (mean), and n is the number of units.

An easier way to calculate inequality is the "inequality index" which I developed and published online in the Journal of Interesting Economics.

First we measure the concentration of the distribution.

Suppose the distribution is (.5, .3, .2) for three persons.

The Herfindahl concentration index is calculated by squaring each fraction: (.25, .09, .04).

Add up the squares: the total in this case is .38.

This is the concentration index C. Let the number of units in the distribution be N.

To get the inequality index I, simply multiply C by N: .38 * 3 = 1.14.

Perfect equality has an index of 1, so the greater the inequality, the greater the index.

For example, for three persons, if one had all and the other two had nothing, the index I equals 3.

Do this inequality problem: (7,3) and (6,1,1,1,1)

Gini: 1 + 1/2 - (2/(4*5))*(7 + 2*3) = 1.5 - .1*(13) = .2

1 + 1/5 - (2/(25*2))*(6 + 2 + 3 + 4 + 5) = 1.2 -.04*(20)=.4

Foldvary index: .49 + .09 = .58, *2 = 1.16; .36+.04=.4,*5 = 2.

Inequality around the world (p. 432).

Table 3, p. 433. Some countries are more and some less unequal than the US.

Brazil an example of high inequality. Why?

Redistribution in countries such as Germany reduces inequality, but at the price of less growth.

Mankiw discusses the political philosophy of redistributing income (p. 437).

1) Utilitarianism: the goal of public policy should be to maximize the utility of the public.

Utilitarianism assumes that there is diminishing marginal utility for wealth.

So extra dollars have less utility if one is rich than if one is poor.

Therefore, redistribution of wealth from the rich to the poor increases utility,

but only so long as that redistribution does not decrease overall wealth too much.

2) Liberalism. Justice requires preventing people from being too poor.

Redistribute to prevent the utility of the poorest from being too low.

It can take the form of a "safety net" of governmental insurance against poverty.

3) Libertarianism. Individuals have natural rights. It morally wrong to redistribute income.

If the initial distribution of income is just, then if economic activity is voluntary, the outcome will be just. It is like the distribution of grades: are grades earned, or "fairly" distributed?

Libertarians advocate equality of opportunity rather than of outcomes.

4) [Not in Mankiw]. Geo-libertarianism. Libertarianism does not answer the question of the just initial distribution of income. Libertarians agree on the rule: to the creator belongs the creation.

Those who earn income by labor are entitled to keep the full wage.

That applies to the product of labor. So there should be no taxes on wages, capital, or sales.

That leaves the question of natural resources. There are two possibilities:

a) Allodial libertarians say we should recognize present-day titles as absolute.

Who ever owns land is entitled to keep all the rent. Allodial means total ownership of land.

b) Geo-libertarians say that present-day land titles are derived from conquest, which is theft.

Moral equality requires an equal benefit from natural resources. The benefit is reflected in rent.

So the rent of land should be shared equally, either as cash or as government services.

This is not a redistribution, but the proper initial distribution.


What is poverty?

Absolute and relative.

Relative: portion of the population at the low end of the distribution of income and wealth.
Absolute: subsistence or less in basic necessities.

US government defines poverty as 3x minimum food expense.

Because rent has increased, % food has decreased to 25%.

But this excludes in-kind transfers such as subsidized housing and medicine.

Median family income in 2000 $50,900.

Poverty line measured at $17,600 for family of four (p. 433).

11.3% are at or below the level.

Since 1970, the percentage in poverty in the US has been about the same.

A female head of household with no spouse present has a poverty rate of 27%.

Why do we continue to have poor people in a rich society?

Partly: unequal wages, lowest wages at subsistence.

Major reason: unequal distribution of non-wage income.

Poverty is basically a very low wage level combined with a highly unequal distribution of wealth.


Policies to reduce poverty (p. 440).

Minimum-wage and "living" wage laws.

It helps some workers at the expense of others who either do not get employed or get lower benefits, since benefits are not subject to minimum wage laws.

Government today does not eliminate the cause of poverty.

Government response has instead been a welfare state.

President Johnson in 1964 declared a war on poverty.

Public assistance, welfare, medicine, food, housing.

Who won the war on poverty? Poverty won.

Problems with redistribution: taxes have disincentives, reducing growth and employment.

Welfare costs rise as more people get on welfare.

The incentive of the poor is to be needy and qualify for welfare.

There is then a large penalty for working: loss of benefits and greater taxes.

Welfare also contributes to family break-up and teenage unmarried mothers.

Result: high taxes, bureaucracy, large welfare class.

The earned income tax credit (EITC) is like a negative income tax for the poor.

Poor working families get a subsidy instead of paying a tax.

There is a great amount of fraud from those getting EITC without really being qualified.

Again, it treats the symptom, not the cause.

What is the ultimate cure for poverty?

The desire of each person to better his or her own condition.

All that is really needed to cure poverty is to avoid putting barriers in the way of self-improvement.

Increase productivity with better training and education.

Shift taxes off labor and enterprise.

Then we can eventually eliminate welfare.

Henry George (1883, p. 78) put the matter very succinctly:
"There is in nature no reason for poverty."
Remove the restrictions and tax barriers, and wages will rise, and poverty will disappear.