Question

A college student decides how many minutes to spend studying for a class. The student talks to her roommate, who is taking the same class, and some of what she learns rubs off. Assume the student’s marginal benefit (demand) curve for Q minutes of studying is, MB=100-Q. If she wasn’t studying then she could hang with friends, and the marginal (opportunity) cost of studying is MC = 2*Q. The roommate receives an external marginal benefit of EMB = ½ * Q.

1. What is the socially optimal level of study?

2. What corrective tax or subsidy could the government set to achieve the socially optimal level of study?

Answer 1

1)

Marginal Social benefit=MSB=MB+EMB=100-Q+1/2Q=100-0.5Q

Marginal Cost=MC=2*Q

Set MSB=MC for socially optimal level,

100-0.5Q=2*Q

Q=40 minutes (socially optimal level of study)

MSB=100-0.2*40=80

2)

Now we estimate the equilibrium without taking EMB into consideration i.e. free market equilibrium

Set MB=MC

100-Q=2Q

Q=33.33

MB= 100-Q=66.67

Subsidy should be granted to reach the socially optimal output.

Subsidy=MSB-MB=80-66.67=13.33