Problem 2: Public Goods [12 Points] Suppose that three individuals each benefit from a public good. The marginal cost of the public good provision is as follows (where Q is the amount of public good purchased): MC = 0.5Q Note here that this MC curve is also shared, so even if Person 2 purchases two units, and then Person 3 wants to purchase a third unit, the MC of this third unit would be $1.5 even if that is the first unit that Person 3 personally buys. Whereas each of the three individuals (Person 1, Person 2, and Person 3] each receive a marginal benefit for each unit of the public good defined by: Person 1: MB, = 21 - Q Person 2: MB2 = 15 - 2Q Person 3: MB3 = 12 - 0.5Q As is the case with public goods, they are non-rival. Therefore, note that each person gains benefit from the total amount of Q, not some individual value (e.g. Q1, Q:, or Q:). 6. Draw all four curves (MC, MB, MB2, and MB;) on a figure with Q on the x-axis and the MC and MBs on the y-axis. Label the x-intercept and y-intercept for all of the MB curves and the x-intercept for the MC curve. [1.5 points] 7. Suppose that each person is completely self-interested, then how much Q would each Person want to purchase if they would have to pay for all of Q themselves? Show your work. [For example, how much Q would Person 2 buy if they would have to pay for all of Q themselves? Do this exercise for each person] [1.5 points] For the next question, when I say is this an equilibrium, I mean that none of the three people have an incentive to either buy more or less of Q. 8. Suppose that the amount of Q purchased is such that Person 3 is exactly indifferent between buying another unit of Q or not. Is this an equilibrium? Why or why not? [Hint: I have purposely not said up until this point which of the three people has purchased the Q, or if and how it is split between them.] [2 points] 9. In this example, draw the Social Marginal Benefit curve. Once again, have Q on the x- axis and SMB on the y-axis. Label the y-intercept and the x-intercept for this SMB curve. Also, label the Q and SMB for both of the points where this SMB is kinked. [3 points] 10. In this example, what is the socially optimal quantity of the public good to purchase? Show your work. [4 points]