Public and Private Goods In a New Year Pary, you need to decide how much money to spend on cans of beer (b, standing for the number of cans of beer) and how much to spend on fireworks (f, standing for the numer of bags of fireworks). A can of beer and a bag of fireworks each have a unit price of $5, that is, $5 gets you one unit of either good. You have $500 to spend, and your utility function is u(f, b) = 10 sqrt(f) + b First, suppose you are spending the New Year holiday alone. (a) How much money will you choose to spend on fireworks, and how much on beer? (b) What is the efficient amount for you to spend on fireworks, and the efficient amount for you to spend on beer? Next, suppose that you are spending the New Year holiday with four of your friends. You can only drink the beer that you bought, but you get to enjoy the sound of fireworks that everyone bought. That is, each of you gets utility u = 10 sqrt(F) + b where F is the total number of fireworks that the five of you collectively bought, while b is still the number of beer you individually bought. (c) Suppose you are perfectly rational and selfish. If you anticipate that each of your friends is going to spend $20 on fireworks, how much would you choose to spend on fireworks and how much on beer? How much utility would this leave you with? (d) Is this efficient? Would you all be better or worse off if you agreed to each contribute $100 to fireworks? Finally, suppose you were spending the New Year holiday at a public park, in a crowd of 500 people (499 others plus yourself). Again, everyone’s utility is 10 sqrt(F) + b, where F is now the amount that everyone in the crowd contributes to the fireworks. (e) If you anticipate that everyone else in the crowd is going to contribute $0.25 each to the fireworks, how much would you choose to spend on fireworks and how much on beer? How much utility would this give you? (f) Is this efficient? Would you be better or worse off if everyone at the park agreed to contribute $25 each toward fireworks? What if everyone at the park agreed to contribute $100 each?