Question

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:



Price

Demand (Millions)

Supply (Millions)

60

22

14

80

20

16

100

18

18

120

16

20



Calculate the price elasticity of demand when the price is $80 and when the price is $100.

Calculate the price elasticity of supply when the price is $80 and when the price is $100.

What are the equilibrium price and quantity?

Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how large will it be?

Answer 1

The price elasticity of demand when the price is $80:

Price elasticity of demand $= \frac{ΔQ}{ΔP} \times \frac{P}{Q}$

$= \frac{-2}{20} \times \frac{80}{20} = -0.4$

The price elasticity of demand at $80 is -0.4

The price elasticity of demand when the price is $100:

Price elasticity of demand $= \frac{-2}{20} \times \frac{100}{18} = -0.556$

The price elasticity of demand at $100 is -0.556

The price elasticity of supply when the price is $80:

The price elasticity of supply $= \frac{ΔQ}{ΔP} \times \frac{P}{Q}$

$= \frac{2}{20} \times \frac{80}{16} = 0.5$

The price elasticity of supply at $80 is 0.5

The price elasticity of supply when the price is $100:

The price elasticity of supply $= \frac{2}{20} \times \frac{100}{18} = 0.555$

The price elasticity of supply at $100 is 0.555

The equilibrium price and quantity are determined at the level were supply is equal to demand.

This happens when price is $100 and quantity is 80 million.

With a price ceiling of $80, consumers are demanding 20 million and producers are supplying 16 million. This will create a shortage in the market.

Shortage = 20 – 16 = 4 million