Question

The inverse of the demand and supply functions for shoes is given by the

following equations respectively:

Demand: P = 1400 - 2Qd

Supply: P = 200 + 1Qs

1.1. Calculate the equilibrium price and quantity of shoes.

(5)

1.2. Assume that the price of shoes is R700. Use your answer in 1.1 to explain

the resulting situation in the market for shoes, and how equilibrium will

be restored without government intervention, ceteris paribus.

(5)

Answer 1

Solution:

1.1.). At equilibrium: Qd = Qs

1400 – 2Q = 200 + 1Q

1400 – 200 = 1Q + 2Q

1200 = 3Q

Q = 400

Equilibrium quantity = 400

Substitute in either the demand or supply function to derive an equilibrium price:

P = 1400 – 2Qd = 1400 – 2(400) = 1400 – 800 = 600

Equilibrium price = 600

 

1.2). The price of R700 will be above the equilibrium price, which means that the quantity of shoes supplied will exceed the quantity of shoes demanded, resulting in a shoe surplus in the market.

 

The market equilibrium will restore itself since the incentives built into the structure of demand and supply will create pressures for the price to decrease toward the equilibrium.