The rent control agency of Rochester has found that aggregate demand is P = 500 –5QD. Quantity, QD, is measured in thousands of apartments. Price, P, equals the monthly rental rate in dollars. The city’s board of realtors acknowledges that this is a good demand estimate and has shown that supply can be expressed as P = 5QS.

a. If the agency and the board are right about demand and supply, respectively, what is the free-market price? How many apartments are rented? 

b. If we assume an average of 3 persons per apartment, what is the expected change in city population if the agency sets a maximum average monthly rent of $100 and all those who cannot find an apartment leave the city?