The City of Cambridge is concerned about the number of wild MIT students who will be partying on Halloween and wants to limit the number of parties in order to curb the costs of policing underage drinking and noise violations. The city has asked you to evaluate the welfare implications of policies they are considering. Think of price here as the amount of money party hosts will collect at the door from party-goers. The demand for parties is given by=3002

. The supply of parties is given by=

Now suppose that the city has found a fail-safe way to tax parties by requiring each party host to pay a fee of $60. Find the new price for party-goers, the after tax price received by the party hosts, and the new equilibrium quantity.

Letbe the price the suppliers receive (after the tax),be the price the consumers pay for each party, andbe the after tax quantity.

calculate the following:

The deadweight loss of the tax:

The consumer surplus post-tax:

Producer surplus post-tax:

Tax revenue:

What happens to total surplus?

What happens to consumer surplus?

What happens to producer surplus?

Suppose instead of a tax, the city requires all parties to obtain a license, and only 50 licenses will be made available for October 31. Assume they can perfectly enforce this policy, and there is no way for a party to happen without a license. What is the new price and quantity?

Let be the quantity after licenses are required andbe the price after licenses are required.=? =?

calculate the following. (Assume that the licenses go to the 50 party hosts with the marginal willingness to supply at the lowest prices.)

The deadweight loss of the policy:

The consumer surplus:

Producer surplus:

What happens to total surplus (relative to no-policy, no-tax)?

What happens to consumer surplus?

What happens to producer surplus?

How would the welfare impact differ if the licenses were allocated randomly among all potential party hosts rather than giving the licenses to those willing to supply at the lowest prices? (Assume that licenses cannot be resold.)

Which policy would potential party-goers prefer?

Which policy would potential hosts prefer?(Consider the marginal willingness to supply of various potential hosts. Assume the 50 licenses are allocated to the hosts with lowest MWTS. Assume the hosts care only about producer surplus. .)

Which policy does the city government prefer?

(Assume that the city will spend $20 on average policing each party and that the city only cares about tax revenue less policing costs not producer surplus, consumer surplus, or deadweight loss.)