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. 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 price and quantity? the deadweight loss of the policy, the consumer and producer surplus, what happens to the total, consumer and producer surplus. Also, 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.)