Price Ceiling (Municipal Rent Control): Suppose we are interested in the housing market. Demand is given by QD = 15 - 3P; supply by QS = 4P - 8. a. Find the equilibrium price and quantity in a perfectly competitive market. Also, find consumer surplus, producer surplus, and total surplus. Plot your results. b. Suppose the municipal government implements a price control, pcontrol = 11/5. Find the new equilibrium, change in consumer surplus, change in producer surplus, and deadweight loss. Plot your results. Does the price control help or hurt consumers? c. Instead, suppose the government desires to keep the price control while also eliminating the shortage in housing. In order to achieve this objective, the government implements a housing voucher to supply additional housing to cover the shortage. [HINT: Think of the voucher as adding a constant to market supply.] What happens to consumer surplus, producer surplus, and deadweight loss? How much does the government have to spend?