Question

The demand curve for a product is Q = 50 – 0.5P. What is the price elasticity of demand at a price of $60?

Answer 1

Answer:

-1.5

Explanation:

              Q = 50 – 0.5P

The formula for elasticity of demand is

              E   = -P/Q x dQ/dP

To find dQ/dP you need to differentiate Q with respect to p.

       dQ/dP  = -0.5

When      P   = 60

                Q  =  50 - 0.5(60)

                Q  =  50 - 30

                Q  =  20

                 E  = -P/Q x dQ/dP

                 P  = 60

                 Q  =  20

          dQ/dP = -0.5

                 E   = -60/20 x (-0.5)

                 E   = -3 x (-0.5)

                  E   = -1.5

Answer 2

The price elasticity of demand at a price of $60 is -1.5

Price elasticity of demand is the degree of responsiveness of price to change in quantity demanded . It is computed as :

E  = -P / Q x dQ / dP

Given that :

Q = 50 – 0.5P

We will need to differentiate Q with respect to p to get dQ/dP

Q = 50 – 0.5P

dQ/dP  = -0.5

When :    

P   = 60

Q  =  50 - 0.5(60)

Q  =  50 - 30

Q =  20

E  = -P/Q x dQ/dP

P  = 60

Q  =  20

dQ/dP = -0.5

Then,

E   = -60 / 20 x (-0.5)

E   = -3 x (-0.5)

E  = -1.5

Hence, the price elasticity of demand(E) at a price of $60 is -1.5

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