Question

Suppose that the inverse demand curve for a well-known sports car can be expressed as P = 100,000 – 2Q², where price (P) is in pound sterling and quantity (Q) is in number of cars.

A.) What is the price elasticity of demand at a quantity of 100?

B.) Is the demand for these sports cars elastic or inelastic?

Answer 1

A) When Q= 100.

P = 100000 - 2Q²

P = 100000 - 2* 100²

P = 100000-20000

P = 80000

now partial derivate of inverse demand curve.

= -4Q

elasticity = * Q /P

elasticity = -4Q * 100 / 80000

elasticity = -4*100* 100/80000 = -0.5

B) the for these sports cars are inelastic. since the value of the elasticity is -0.5 and when 0<ED<1 , the demand is said to be inelastic.