Problem 2 (Externalities) (30 pts.) There are two people on an island: Tom Hanks and Wilson. Consider the following problem faced by Wilson max UW (W, fW) 1W JW subject to pov" +pif" = MW where " now denotes the consumption of vaccines which protect him from Disease X, f" is consumption of food. po is price of vaccines, py is price of food and M" is money that Wilson has available. Moreover, suppose that Wilson's preferences are represented by the function UW ( OW , fW ) = AW In(u" ) + in(f" ) Tom Hanks's utility is UT (UW, f? ) = Al In(v") + In(f?) and his budget constraint is simply p, ff = MT. Note that there is no v term in Tom Hank's utility because for some rare reason, the vaccine does not work for him. His utility, however, does depend on v", because he likes the fact that Wilson is less likely to infect him with Disease X. 1. What is the market failure in this economy? Describe this specificly and explain briefly why. (5 pts.) 2. Solve for the equilibrium allocation of the competitive equilibrium. (5 pts.) 3. Intuitively, explain why the equilibrium allocation found in part (2) is not efficient. (I am looking for a verbal explanation. There is no need to do math). (5 pts.) 4. Now suppose that government subsidizes vaccines at a rate s and funds this subsidy by lump-sum taxing Tom Hanks. Rewrite the above problems of Wilson and Tom Hanks to account for this and solve for the equilibrium quantities. What happens to Wilson's consumption of vaccines? How does the subsidy potentially solve the market failure? Hint: the subsidy only affects the price of the vaccine p, for Wilson by multiplying it by (1 -s). (5 pts.) 5. Now suppose that there is no subsidy on vaccines but that Wilson is altruistic and cares about the well being of Tom Hanks, so instead of maximizing U"he is maximizing U" + offUff where 0