# Determining the equilibrium rental/quantity of apartments

See the attached file.

The rent control agency of New York City has found that aggregate demand for rental apartments is QD(P)=160-8P. Quantity is measured in tens of thousands of apartments. Price, the average monthly rental rate, is measured in hundreds of dollars. In the short run, the quantity of rental apartments is fixed at Qs=104.

a.If the agency is correct about demand, what is the short run competitive price for rental apartments in this market? What is the price elasticity of demand?

The city's board of realtors has shown that the long run supply of rental apartments is given by Qs(P)=70+7P.

b.Draw a figure for the market for rental apartments. What is the long run competitive price for rental apartments? How many apartments are rented?

c. If the rent control agency sets a maximum average monthly rent of $300, how many renters will be forced to leave the market (assuming one renter per rental apartment) relative to the competitive equilibrium? Show the price ceiling on your figure.

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#### Solution Preview

Please refer attached file for graphs.

a) Qd=160-8P

Qs=104

In equilibrium Qd=Qs

160-8P=104

8P=56

P=$7 hundred per month

Qd=160-8P

Differentiating with respect to P, we get

dQd/dP=-8

Price elasticity of demand=(dQd/dP)*(P/Q)=-8*(7/104)= -0.53846

Short run rental price=$700 per ...

#### Solution Summary

Solution determines the short run and long run equilibrium parameters.