Question

1 Externalities I Consider the market for private economics mentor in Davis. Assume it is perfectly competitive. The market’s inverse demand curve is p = 1600 − 5Q, with Q being the number of students receiving mentor per quarter and p being the price per quarter. Economics mentors’ private marginal cost curve is MCP = 100 + 5Q. Also assume that, because economics professors curve their classes, when one student improves her grade, it causes every other student to have a lower grade. This is a negative externality. Assume the marginal cost of curving is MCC = 2.5Q.

1. Please find the un-regulated monopoly equilibrium of this market.

2 Please draw this market, including the following curves— demand, marginal revenue, private marginal cost, and social marginal cost. Also, label the following points—the unregulated monopoly equilibrium and the socially optimal equilibrium. Also please label axes and where curves cross axes.

3. What is deadweight loss in this market? Now suppose that the City of Davis wants to ensure the socially optimal equilibrium in this market by imposing a standard.

4. What standard should the City of Davis set?

Answer 1

Q1) at unregulated Monopoly

MR = PMC

1600-10Q = 100+5Q

1500 = 15Q

Q* = 100, P* = 1600-5*100 = 1100

So eqm, Q* = 100, P*= 1100

2) at socially efficient equilibrium,

PMB (private marginal benefit) = SMC

SMC = PMC + MEC = 100+5Q+ 2.5Q = 100+7.5Q

So at eqm, 1600-5Q= 100+7.5Q

1500 = 12.5Q

Q* = 120

Q3) deadweight loss = .5*(1225-850)*(150-120)

= .5*375*30

= 5625

Q4) standard set = produce 120 units .