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 byQ=3002p

. The supply of parties is given byQ=p

.

Find the equilibrium price and quantity in the market for Halloween parties.

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.

Letp

s

be the price the suppliers receive (after the tax),p

c

be the price the consumers pay for each party, andQ

t

be the after tax quantity.

The deadweight loss of the tax?

The consumer surplus post-tax?

Producer surplus post-tax?

Tax revenue?

Show the welfare impact of this policy in a graph. In your graph, label regions corresponding to (total) producer surplus post-tax, (total) consumer surplus post-tax, tax revenue, and deadweight loss post-tax.

(Your graph is not graded, but you can check your answer. It is for your own understanding.)

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?

LetQ

L

be the quantity after licenses are required andp

L

be the price after licenses are required.

For the quantity restriction in PS6.2.4, 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?

Show the welfare impact of this policy in a graph. In your graph, label regions corresponding to (total) producer surplus, (total) consumer surplus, and deadweight loss.

(Your graph is not graded, but you can check your answer. It is for your own understanding.)

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?

Which policy does the city government prefer?