Question

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

Price (dollars) Demand (millions) Supply (millions)

60 22 14

80 20 16

100 18 18

120 16 20

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

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

price is $100.

c. What are the equilibrium price and quantity ?

d. Suppose the government sets a price ceiling of $80. Will there be a shortage,

and if so, how large will it be ?

Answer 1

Answer and Explanation:

A. Price elasticity of demand

Price(P0) = $80 , Q0 = 20

Price(P1) = $100 , Q1 = 18

Price elasticity of demand =

$\frac{\frac{Q1-Q0}{\frac{Q1+Q0}{2} } }{\frac{P1-P0}{\frac{P1+P0}{2} } } \\\\\frac{\frac{18-20}{\frac{18+20}{2} } }{\frac{100-80}{\frac{100+80}{2} } }\\\\\frac{\frac{-2}{\frac{38}{2} } }{\frac{20}{\frac{180}{2} } }\\\\\frac{\frac{-2}{19} }{\frac{20}{90} } }\\\\-0.47$

Price elasticity of demand = 0.47

B. Price elasticity of supply

Price(P0) = $80 , Q0 = 16

Price(P1) = $100 , Q1 = 18

Price elasticity of supply =

$\frac{\frac{Q1-Q0}{\frac{Q1+Q0}{2} } }{\frac{P1-P0}{\frac{P1+P0}{2} } } \\\\\frac{\frac{18-16}{\frac{18+16}{2} } }{\frac{100-80}{\frac{100+80}{2} } }\\\\\frac{\frac{2}{\frac{34}{2} } }{\frac{20}{\frac{180}{2} } }\\\\\frac{\frac{2}{17} }{\frac{20}{90} } }\\\\0.53$

Price elasticity of supply = 0.53

C. The point , where Demand and supply is equal called equilibrium price

So , $100 is equilibrium price.

D. if market price is less then equilibrium price , it is effective So, shortage (20-16) 4 units