Question

The demand and supply of apartments in Vancouver are given by (Demand) P = 1200 − 2Q and (Supply) P = 2Q.

(a) Find the equilibrium price P ∗ and quantity Q∗ . Compute the consumer surplus and producer surplus.

(b) Suppose the city government decides to implement rent control with the price set at $400. Illustrate the effect (if any) this has on the equilibrium outcome. Additionally, calculate any shortage or surplus that may exist and indicate this on the illustration (if no shortage or surplus exists, illustrate this as well).

(c) As the Olympic Village apartments become available, suppose the supply curve shifts to become P = Q. Find the new equilibirum price P ∗ and Q∗ . Is the rent control price more or less restrictive for the market than in the previous case?

Answer 1

The equilibrium price and quantity are $600 and 300 units, respectively. Rent control at $400 creates a 600-unit shortage. With the new supply curve P = Q, the rent control price of $400 becomes the market equilibrium, rendering rent control non-restrictive.

Step-by-step explanation:

Finding the Equilibrium Price and Quantity

To find the equilibrium price P* and quantity Q*, we set the demand and supply equations equal to each other: 1200 − 2Q = 2Q. Solving for Q gives us 1200/4 = 300, so Q* = 300 units. Substituting this into either the demand or supply equation gives us P* = $600.

The consumer surplus is the area above the price and below the demand curve, while the producer surplus is the area below the price and above the supply curve. To calculate these, we would need the intersections of the demand and supply curves with the price axis, which can be obtained from the equations by setting Q to zero.

Effect of Rent Control at $400

With rent control at $400, the quantity supplied would be Qs = 200 units (from P = 2Q), and the quantity demanded would be Qd = 800 units (from P = 1200 − 2Q). This creates a shortage of 600 units since demand exceeds supply at this controlled price.

New Equilibrium with Shifted Supply Curve

The new supply equation P = Q leads to a new equilibrium where Q* = 400 units and P* = $400. With this new supply curve, the rent control price becomes the market equilibrium price, which means it is no longer restrictive as both the controlled price and the market price are the same.