Hsiang lives in a densely populated city in China. His utility depends positively on two things, the consumption of a composite good (X) and his health (H), and negatively on air pollution (P). His income is given: Y = 10. The price of X is 1. His health is affected directly by air pollution (P), but he can improve it by making defensive expenditure (D), such as buying an air filtering system for his home. Let us assume U (X,P,H) = X H – 2 P D (P,H) = 1/3PH^3 Write your numerical results up to two decimal points. a) Suppose that P = 3. Write Hsiang’s maximization problem. Draw the budget constraint and several indifference curves. b) Calculate the optimal amounts of X and H for Hsiang, and his resulting utility. c) Now suppose a new air filtering system is available on the market. It is supposed to be more efficient than previous filters. If Hsiang decides to buy it, his defensive expenditures become D (P,H) =PH^ 2. Calculate the optimal utility level that Hsiang can attain if he buys this new system. Should he take this decision? d) Suppose that Hsiang finds a new well-paid job, so that his income is raised to Y = 100. Compare the utility levels that he can reach using each filtering system. Which one should he adopt? e) Explain why poor people have a lower marginal willingness to pay for better health (or for an improved environmental quality).