Consider the market for education. The marginal social cost of education (MSC) a
ID: 1194491 • Letter: C
Question
Consider the market for education. The marginal social cost of education (MSC) and the marginal private benefit of education (MPB) are given by the following equations where Q is the number of units of education provided per year. MSC = 10 + Q
MPB = 100 – Q
You are also told that each unit of education provides an external benefit to society of $10 per unit. This external benefit is currently not being internalized in the market
e) Suppose that the external benefit is internalized in this market when the government provides a subsidy of $10 per educational unit to consumers. What will be the socially optimal amount of education to provide given this subsidy?
f) Given the subsidy in (e), calculate the value of consumer surplus with the subsidy (CS’), producer surplus with the subsidy (PS’). With the subsidy there are no longer any external benefits that the market fails to account for. Sum together CS’ + PS’:
Explanation / Answer
MSC = 10 + Q
MPB = 100 - Q
(e) When external benefit is internalized, MPB increases by $10.
Internalized MPB = 100 - Q + 10 = 110 - Q
The social optimal is obtained by equating MSC with Internalized MPB:
10 + Q = 110 - Q
2Q = 100
Q = 50
Internalized MPB = 110 - Q = 110 - 50 = 60
(f)
For MSC curve: When Q = 0, MSC: 10 [Vertical intercept]
For Internalized MPB: When Q = 0, Internalized MPB = 110 [Vertical intercept]
Socially optimal price = 60, Q = 50
CS' = (1/2) x (110 - 60) x 50 = 1,250
PS' = (1/2) x (60 - 10) x 50 = 1,250
CS' + PS' = 1,250 + 1,250 = 2,500