Answer to Question #273190 in Microeconomics for Suhaaa

Question

There are two workers. Each worker’s demand for a public good is P =
20 -

Q. The marginal cost of providing the public good is $24. The accompanying graph summarizes the relevant information.

a. What is the socially efficient quantity of the public good?

b. How much will each worker have to pay per unit to provide the socially

efficient quantity?

Answer 1

In case of a public good, same quantity of public good is provided to each consumer and they pay a price according to their demand schedule. In the case given, there are two workers and they have a same demand curve P=20-Q. This implies that both the workers face the same price. The corresponding figure for this case is Figure A-1 below

Figure A-1

a)

To determine the price and quantity of the public good, compute the combined demand of both workers:

P=20-Q+20_Q

=40-2Q

The socially efficient level of public good occurs at a point where the marginal cost of producing it equals the total demand for it. Hence equilibrate total demand with the marginal cost:

P=MC

40-2Q=24

2Q=16

Q=8 and P=$12

Hence the socially efficient output level is 8 units.

b)

Workers as individual can pay $12 for 8 units of public good but the marginal cost of providing 8 units is $24. Hence individually they are not able to pay for it.

But if each of them is willing to pay $12 jointly, they can together pay $24 and thus will be able to afford the socially efficient level of output.

Hence each worker will have to pay $12 per unit to provide socially efficient quantity.