Question

Consider a college town where the initial price of rental apartments is $500 and the initial quantity is 3,000 apartments. The price elasticity of demand for apartments is 1.25, and the price elasticity of supply of apartments is 0.75.

a) Use demand and supply curves to show the initial equilibrium, an label the equilibrium point a.

b) Suppose that an increase in college enrollment is expected to increase the demand for apartments in the college town by 30 percent. Use your graph to show the effects of the increase in demand on the apartment market. Label the new equilibrium point b.

c) Predict the effect of the increase in demand on the equilibrium price of apartments.

d) Find the new equilibrium quantity given the new price.

Answer 1

a.

b.

Increase in demand leads to the shift in the demand function and the new equilibrium point 'b' is given by the following curve:

i.e more quantity will be demanded for the same price due to the shift in the demand function.

c.

Since price elasticity of demand is given by the formula :

% change in quantity/% change in price = 1.25

[Q2-Q1/Q1]/[P2-P1/P1] =1.25

and the price elasticity of supply is given by the formula :

% change in quantity/% change in price = 0.75

[Q2-Q1/Q1]/[P2-P1/P1] = 0.75

and we know P1 = 500 $ and Q1 = 3000 units

i.e

Q2-3000/3000 * 500/P2-500 = 5/4 &

Q2 -3000/3000 * 500/P2-500 =3/4

Q2-3000/6(P2-500) = 5/4 &

Q2 -3000/6(P2-500)= 3/4

Solving

9P2 -1500 = 15P2 -7500

i.e 6P2 = 6000

P2 = 1000 $

and Q2 = 13500/2 = 6750 units

hence the new equilibrium Price = 1000 $ and equilibrium quantity = 6750 units