Answer to Question #273182 in Economics for Suha

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?

c. Suppose the two workers contribute the amount needed to provide the quality of public good you identified in parts (a) and (b). A third worker values the public good just like the two contributing workers, but she

claims not to value the good because she wants to “free ride” on the pay-

ments of the other two workers.

(1) Given the three workers’ true demands for the public good, is the amount

of the public good provided by the two workers socially efficient?

(2) Compare the level of consumer surplus enjoyed by these three workers.

Which worker(s) enjoys the most surplus?

Answer 1

a. The socially efficient quantity of the public good is:

P = MC,

The total demand is: Q = 2(20 - P) = 40 - 2P.

P = 20 - 0.5Q,

20 - 0.5Q = 24,

Q = -8 units or no output will be produced, but the socially efficient quantity is positive.

b. Each worker will have to pay more than the market priceper unit to provide the socially

efficient quantity.

c.

(1) Given the three workers’ true demands for the public good, the amount of the public good provided by the two workers is not socially efficient.

(2) The level of consumer surplus enjoyed by the first two workers will decrease.

The third worker enjoys the most surplus.