ECON 448: Week 8-

1. Inequality Measures

(1) Gini Coefficient (Index) = The ratio of the area between the Lorenz curve and the 45^o line of perfect equality, to the area of the triangle below the 45^o line.

(2) Among the measures of inequality, the mean absolute deviation fails the Dalton principle, while the coefficient of variation satisfies all of the four principles for inequality measurement and is consistent with the Lorenz criterion.

2. Inequality and Development: Interconnections

1. Consider an economy of 10 people and two sectors (modern and traditional) with yearly incomes equal to $1,000 and $2,000. Suppose that all growth proceeds by moving people from traditional to the modern sector.

(a) Plot values of the Gini coefficient and the coefficient of variation as individuals move from the traditional to the modern sector.

The Coefficient of Variation:

C = 1/µ √(_j=1∑^mn_j/n(y_j - µ)²)

The Gini Coefficient:

G = 1/2n²µ _j=1∑^m_k=1∑^mn_jn_k|y_j - y_k|

(b) Can you invent a Lorenz-consistent inequality measure which does not display the inverted-U property in this case?

2. This problem tests your understanding of the income distribution on savings rates.

The economy of Sonrisa has people in three income categories: poor, middle class, and rich. The poor earn $500 per year and have to spend it all to meet their consumption needs. The middle class earn $2,000 per year, of which $1,500is spent and the rest saved. The rich earn $10,000 per year, and consume 80% of it, saving the rest.

(a) Calculate the overall savings rate in Sonrisa if 20% of the people are poor and 50% are in the middle class.

(b) Suppose that all growth occurs by moving people from the poor category to the middle-class category. Will the savings rate rise over time or fall? Using the Harrod-Domar model and assuming that population growth is zero and all other variables are exogenous, predict whether the resulting growth rate will rise or fall over time.

(c) Outline another growth scenario where the rate of growth changes over time in a way opposite to that of (b).

(d) Understand well that this question asks you about how growth rates are changing. In the simple Harrod-Domar model, the growth rate is constant over time because the savings rate is presumed to be unchanging with the level of income. Do you understand why matters are different here?

3. Explain why a one-time redistribution of land is likely to have less of a negative effect on investment rather than a redistribution of income period after period (but with a similar distribution of present values of assets as the land redistribution).