Find the price elasticity of demand for the demand function at the indicated x-value?

Question

Demand function: p=700-3x

Quantity Demanded: x=15

(a) Find the price elasticity of demand for the demand function at the indicated x-value.

(b) Identify the intervals of elasticity and inelastcity

Answer 1

p = 700 - 3x

p + 3x = 700

3x = 700 - p

x = (700 - p)/3 <--- demand in terms of price

= (-1/3)p + 700/3

For x=15, p = 700 - 3(15) = 700 - 45 = 655

(15,655)

Increase 655 by 1% is 661.55

the demand at =661.55 is x=12.816

D.E.P = (15 - 12.816)/(655 - 661.55) = -0.3 = -1/3

so, no significant change in demand per 1% change in price

dQ/dx = -1/3

dP/dx = -3

dQ/dP = 1/9