Question

Given the following demand function: P=1000-20Q

Where: P: price in US $ Q: monthly sales

a) What is the price elasticity of demand at a price of $500?

b) At what price, if any, is the price elasticity of demand equal to one?

Answer 1

(A)At P=500

Equilibrium quantity

500=1000-20Q

Q=25

Elasticity of Demand = (-1/slope)(P/Qd) -equation(1)

Qd= quantity demanded

P=1000-20Q

Slope=-20

Q=25

P=500

Putting all these value in formula of Elasticity of Demand which is stated as equation(1)

= [-1/(-1/20)][500/25]=400

(B) let’s assume equilibrium is at initial quantity 25unit

To find out price at price elasticity of demand equal to 1 let’s assume price=P

Putting value in equation 1

[-1/(-1/20)][P/25]=1

20P/25=1

P=25/20=1.25

At P=1.25 and Q=25 price elasticity of demand =1