Suppose you are studying a community that has 10 individuals. Each individual has the utility function U(c, p) = c + ln(p).
a. Suppose each individual has an income of 30. P is a unique good because its a public good. This means that if I purchase police, my neighbors gets to consume whatever I purchase, and vice versa. How much c does each individual consume consume, and how p does everyone consume if the price of c is 2, and the price of p is 20?
b. What is the socially optimal level of P, based on the Samuelson condition?
c. How does your answer to part b, compare to a? What is a way we could get people to purchase more police?