Question

1. The rent control agency of New York has determined the demand for apartments to be

Q_D = 160 - 8P

Where quantity is in tens of thousands of apartments and price is the average monthly rental rate in hundreds of dollars. The agency has determined that the supply of apartments is given by

            Q_S = 70 + 7P

1. Find the equilibrium price and quantity if the agency does not regulate the rental rate.
2. Suppose the agency sets a monthly rental rate of $300.00. How many apartments are rented?
3. Suppose the city’s board of realtors requests and receives a rental rate of $900/month. How many apartments are rented?
4. Which of these regulated rental rates results in the lower deadweight loss of Economic Surplus? What is that deadweight loss?

Answer 1

a) Equilibrium under no regulation has Qs = Qd

70 + 7P = 160 - 8P

15P = 90

P = 600 per month

Q = 1,120,000 apartments

b) At P = 300, we have Qd = 160 - 8*3 = 1,360,000 apartments while Qs = 70 + 7*3 = 910,000 apartments. Hence there is a shortage of 450,000 apartments. A total of 910,000 apartments are rented at a rent of $300 per month

c) At P = 900, we have Qd = 160 - 8*9 = 880,000 apartments while Qs = 70 + 7*9 = 1,330,000 apartments. Hence there is a surplus of 450,000 apartments. A total of 880,000 apartments are rented at a rent of $900 per month

d) Deadweight loss from P = 300 is DWL = 0.5*(8.625*100 - 3*100)*(1120000 - 910000) = 59.0625 million

Deadweight loss from P = 900 is DWL = 0.5*(9*100 - 2.571*100)*(1394320 - 880000) = 165.32 million

Hence lower deadweight loss is from P = 300 which is 59.0625 million