Question

The social marginal cost of producing a certain public good is $20 per unit. Society consists of three individuals. Persons 1, 2, and 3 value the public good according to the following marginal benet schedules: MB1 = 60 − Q, MB2 = 120 − 3Q, and MB3 = 150 − 2Q, where Q denotes the number of units of the public good provided. Assume that, at any quantity Q that makes a person's marginal benet become negative, that person's MB = 0. For example, MB1 = 0 for Q ≥ 60.

(a) Draw the individual marginal benet curves, the social marginal benet curve, and the social marginal cost curve on the same diagram. Label the slopes and y-intercepts. [2 marks]

(b) Determine the ecient quantity of the public good. [2 marks]

Answer 1

a) For social marginal benefit, add all the marginal benefits. This makes social marginal benefit =  MB1 + MB2 + MB3

Slope of MB1 is -1, slope of MB2 is -3 and that of MB3 is -2. Slope of SMB is -6.

b) Efficient quantity is when SMB = SMC From the graph we see that it lies between 60 and 70 and precisely it is 65

Q	MB1	MB2	MB3	SMB
0	60	120	150	330
10	50	90	130	270
20	40	60	110	210
30	30	30	90	150
40	20	0	70	90
50	10	0	50	60
60	0	0	30	30
70	0	0	10	10
80	0	0	0	0