1)(8pts) Market interventions: SF Rent Control

a)(3pts) The demand for housing in San Francisco for a two bedroom apartment in the Russian Hill area is given by Q_d= 380,000 - 120R + 0.4P_H +2Y, where P_H is the median price for two bedroom homes in the same area.Suppose P_H is $1,500,000, and Y is average annual income for residents of this area, which is $200,000. The supply equation is Q_s = -20,000 + 80R, where R is monthly rent. Find and graph the inverse demand functions.What is the equilibrium rent, R*, and quantity of housing on the market, Q*?

b)(2pts) What happens when we institute rent control: rents are capped at R=$4,000 per month.What is Q^S?How much is the resulting shortage?Where will these people live?

c)(3pts) Using your answers in (a) and (b) draw a graph showing the welfare effects of rent control.Calculate the deadweight loss caused by the rent cap.