Consider Arturo, an individual with utility for a composite good () and

indoor air quality (): = . Indoor air quality depends on pollution levels outside

() and defensive expenditures (): = . Let Arturo's income be .

(a) Write Arturo's problem of utility maximization subject to a budget constraint

mathematically. Draw Arturo's budget constraint and several indifference curves.

(b) Suppose = 10 and = 1. What are the optimal amounts of and for

Arturo?

(c) What happens to the optimal and (show your work) when (i) increases

to 2 and (ii) Y increases to 20?

(d) It is observed that low-income individuals are exposed to more pollution. Is the

answer to part(c) consistent with this?