Suppose that three individuals each benefit from a public good. ...

Suppose that three individuals each benefit from a public good. 

The marginal cost of the public good provision is fixed at $15 per unit: MC = $15 

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: MB1= 30 − 2Q 

Person 2: MB2= 20 − 2Q 

Person 3: MB3= 21 − Q 

As is the case with public goods, they are non-rival. Therefore, note that each person gains benefit from the total amount of Q purchased by everybody, not just the individual value that they purchase themselves (e.g. Q1, Q2, or Q3). 

1. Draw a figure with all three MB curves, the MC curve, and the Social Marginal Benefit (SMB) Curve. Label all x-intercepts, y-intercepts, and kinks in the SMB curve

2. Given the above MB curves, write down the Social Marginal Benefit Curve as a function of Q. Show your work. 

3. What is the Socially Optimal Choice of Q and would any private individual purchase this on their own? Show your work. 

Suppose that you are on the town council, and that the town currently has Q = 11 of this public 
good. You are considering raising money from Persons 1 - 3 in order to buy another unit of Q, 
where Person 1 pays t1, Person 2 pays t2, Person 3 pays t3 (t1, t2, and t3 can all be different). 
4. Propose a set of taxes (t1, t2, t3) such that they both (i) raise enough money to buy the 
extra unit of Q, and (ii) that they make each person strictly better off. Show your work. 
 

please show graph as well