Suppose that three residents of a town would get marginal benefits from a pure public good given by the following equations:

MB₁ = 20-2Q

MB₂ = 20-2Q

MB3 = 10 Q

Suppose that this public good costs $30 per unit.

(a)(10 points) If each resident purchased the good separately, how much would each resident purchase? Briefly Explain.

(b)(10 points) Solve for the equation that represents the marginal social benefits for the three residents.

(c)(10 points) What is the socially optimal amount of the public good?

(d)(10 points) Suppose that each resident was assigned a tax $10, and the quantity purchased would be determined by majority vote. What quantity would be purchased?