Question

The social marginal cost of producing a certain public good is $20 per unit. Society consists...

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]

Homework Answers

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
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