Question

17.21. Consider an economy with two individuals. Individual 1 has (inverse) demand curve for a public good given by P1 = 60 - 2Q1, while Individual 2 has (inverse) demand curve for the public good given by P2 = 90 - 5Q2. The prices are measured in $ per unit. Suppose the marginal cost of producing the public good is $10 per unit. What is the efficient level of the public good?

Answer 1

Market demand for a vertical good is the vertical summation of individual demand curves. So,
P = P1 + P2 = 60 - 2Q + 90 - 5Q = 150 - 7Q
(Because Q1 = Q2 = Q)

Now, P = MC gives,

150 - 7Q = 10
So, 7Q = 150 - 10 = 140
So, Q = 140/7
So, Q = 20

The efficient level of the public good is 20 units.