Question

Demand for education is characterized by the following equation: P = 240 – 4Q. The marginal private cost of education is P = 40 + 6Q. Production of education also creates a per unit positive externality equal to 2Q. Suppose that the market is currently unregulated (i.e., the positive externality is not currently being corrected for in the market). What is output and price? The marginal social benefit (MSB) accounts for the marginal private benefit of production as well as for the additional benefits received by the society. What is the MSB equation for production of education? What is the socially optimal level of output and price?

Answer 1

Given: demand for education: P=240-4Q

Marginal Private Cost (MPC): P=40 + 6Q

Positive externalities would be created out of it: 2Q

Case 1) Since, the market is currently unregulated and positive externality is not corrected in the market, hence market is producing where MPC=MPB as well as MPB=MSB.

Hence in given case MSB= MPC= 40+6Q.

Case 2) Otherwise, when positive externalities implemented, then MSB = MPB+ Positive Externaities (External Benefits)- External cost,  

Hence in given case MSB= 40+6Q +2Q= 40+8Q

Output (Q) and Price (p) calculation:

in given scenerio:

equate 240-4Q=40+6Q,

4Q+6Q=240-40

Q= 20,

P=160.

Social Optimal level of output and price

For social optimal level MSC=MSB.

In given case= MSB= 40+6Q +2Q, where Q= 20 (put Q=20 in given equation)

here, MSB= 200

But according to demand equation, P=240-4Q, Optimum cost is 160.

this is not the case of socially optimum level of output and price