P= -0.02x^2 -0.2x+6

Question

Compute the elasticity of demand when x = 6. (Round your answer to two decimal places.) 



Answer 1

let x=q be the quantity demanded

P = -0.02 x^2 - 0.2x + 6 = -0.02 q^2 - 0.2 q + 6

dP = -0.04q - 0.2 dq

-1/(0.04q + 0.2) = dQ/dp

The elasticity then is

q=6 --> 1/(0.04*6 + 0.2)

= 1/(2.4+0.2)

= 1/(2.6)

= reciprocal ( 26/10)

= reciprocal (13/5)

= 5/13

so the demand changes by 5 and the price changes by 13

when 6 are demanded