4. Suppose a city consists of blacks and whites. White household income is distributed uniformly between 0 and 100; black income, between 0 and 60.

There are three schools: two that whites attend and one that blacks attend.

Racial segregation is perfect, and among whites income segregation is also perfect. The two white schools are of equal size.

a. What is the average income in the black school?

b. What is the average income in the poor white school? The rich white school?

c. Consider only kids from households below the white median income.

What is their average income in the school that white kids attend? What is their average income in the school that black kids attend?

d. Consider only kids from households above the white median income. What is their average income in the school that white kids attend? What is their average income in the school that black kids attend?

e. Since peer effects matter, would you expect a bigger racial test-score gap among richer children or poorer?