Question

Suppose that consumers A and B have the following marginal benefit schedules for the public good G: MB(A)=50-2G MB(B)=40-3G.

(i) Suppose there are 4 units of the public good. What is the marginal benefit to consumer B of an additional unit of the public good?

(ii) What is the total benefit to consumer B from consuming 4 units of the public good? Draw a graph to illustrate this total benefit. Show your calculations.

(iii) If the marginal cost of providing an additional unit of public good is $40 (i.e. MC = 40). What is the efficient quantity of the public good? Draw a graph to illustrate the social marginal benefit schedule, the marginal cost and the efficient level of the public good. Show your calculations.

Answer 1

After plotting the different values of G with respect to total benefits (calculated by inserting these values of G in equation 1), we get the following total benefits schedule for consumer B:

(iii) MC=40G, Social marginal benefits would be the summation of individual marginal benefits. Hence, SMB= MB(A) + MB(b) = 50-2G+40-3G= 90-5G.

SMB= 90-5G.

The efficient level of the public good would be determined where social marginal benefits (SMB) intersects with the marginal cost curve.

We plot SMB and MC at different values of G, and we get the following schedule...

From the above graph, it is clear that SMB=MC at G=2. Hence, the efficient level of the public good would be 2.