Question

Consider the market for private economics tutors in Davis. Assume it is perfectly compet itive. The market's inverse demand curve is p = 1600 - 5Q, with Q being the number of students receiving tutor per quarter and p being price per quarter. Economics tutors' 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 Q Now assume that one private economics tutor takes over the entire market because the tutor has a lower marginal cost than any other tutor. So now the market has a monopoly. But assume that the demand and marginal cost curves stay the same. 2.1 Please find the un-regulated monopoly equilibrium of this market 2.2 Please find the socially optimal equilibrium of this market 2.3 Please draw this market, including the following curves- demand, marginal revenue, private marginal cost, and so- cial marginal cost. Also label the following points-the un- regulated monopoly equilibrium and the socially optimal equi- librium. Also please label axes and where curves cross axes 2.4 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 2.5 What standard should the City of Davis set? Now suppose that instead of a standard the City of Davis wants to impose a specific tax on this market to ensure the socially optimal equilibrium 2.6 What specific tax should the city of Davis set? Now assume that due to a policy change, economics professors start curving more strictly and the negative externality in the market for private economics tutors increases. 2.7 What would the marginal cost of curving need to be for the un-regulated monopoly equilibrium to be the socially optimal equilibrium?

Answer 1

A) P = 1600-5Q

MR = 1600-10 Q

At monopoly eqm, MR = MC

1600-10 Q= 100+5Q

1500 = 15Q

Q* = 100, P* = 1600-500 = 1100

2.2) socially optimal eqm

SMC = PMC + MEC

= 100+5Q + 2.5 Q

= 100+7.5Q

Then at eqm :

PMB = SMC

1600-5Q = 100+7.5Q

1500 = 12.5Q

Q* = 1500/12.5 = 120

2.3) graph

deadwt SMC 1600 1100 PMC 50 PM (dd Cuorve) PMB 100 MR. 320 100120160

2.4) at Q=100, SMC = 100+7.5*100 = 850

deadweight loss =

.5*(1100-850)*(120-100)

= 250*20*.5 = 2500

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