Jack shares a small apartment with some roommate. There are many cans of baked beans in the pantry. Jack is very hungry, and consumption of baked beans yields marginal benefits to Jack of 16-3Q, where Q is the number of servings of beans. The beans make Jack's stomach hurt, with marginal costs to Jack of 2+.5Q. Unfortunately, this stomach ache also impacts Jack's roommates, the MSC of his bean consumption is 6+2Q.

a. How many beans will Jack consume on his own?

b. What is the socially efficient quantity of bean consumption?

c. What is the deadweight loss at the equilibrium?

d. If Jack's roommates force him to pay them a per-serving bean tax whenever he consumes the beans, how much should the tax be to maximize welfare for the society?