2. The Dalton transfer principle may not be a good way to judge increases in polarization (for a definition, see Esteban and Ray [1994] and Wolfson [1994]). To see this, begin with a society in which incomes take all values in $100 increments between $100 and $1000, and in which an equal proportion of the population (1/10) occupies each of these classes. Show this income distribution in a diagram with incomes on the horizontal axis and population proportions on the vertical axis. Now draw another diagram with half the population at the income level $250, and another half at income level $750. Intuitively rank these two income distributions: which one has more scope for social unrest, which one might display a greater awareness of inequality, and so on.

Now show that the second distribution can be obtained by a sequence of progressive Dalton transfers from the first. Do you feel that your intuition is in line with the transfer principle, in this example?

3. Are the following statements true, false, or uncertain? In each case, back up your answer with a brief, but precise explanation.
   1. The Kuznets ratios satisfy the Dalton transfer principle.
   2. If the Lorenz curve of two situations do not cross, the Gini coefficient and the coefficient of variation cannot disagree.
   3. If a relatively poor person loses income to a relatively rich person, the mean absolute deviation must rise.
   4. The Lorenz curve must necessarily lie in the lower triangle of the diagram, bounded by the 45 line at the top and the axes at the bottom.
   5. The ethical principles of inequality measurement anonymity, population, relative income, and transfers are enough to compare any two income distributions in terms of relative inequality.
   6. If everybodys income increases by a constant dollar amount, inequality must fall.