Elasticity of demand

Question

Find the elasticity of demand for the demand function x=500-2p^2 when the price per unit p is $10. The elasticity of demand is:

Answer 1

x=500-2p^2 = 500-2(10)^2 = 500-200= 300

x' =- 4p = -4(10) = -40

price elasticity of demand =(dx/dp)/x/p = x'p/x =-4p^2/(500-2p^2) = -40(10)/300 =-400/300 = -4/3

but traditionally the negative sign is dropped, so elasticity = 4/3

at price =10, elasticity = 4/3 = 1.333...

at about price = 9.13, elasticity is unit elastic = 1

x'p/x = -4p^2/(500-2p^2 = -1

4p^2 = 500-2p^2

6p^2 = 500

p^2 =500/6 = 83 1/3

p = sqr(500/6) = 10sqr(5/6) = about 9.13