Given the demand function Q12020P 05p2 find the price elast

Given the demand function Q=120-20P + 0.5p^2

find the price elasticity of demand at P=4

Solution

Q = 120 - 20P + 0.5P²

dQ/dP = -20 + P

At P = 4,

Q = 120 - 20*4 + 0.5*4*4 = 48

& dQ/dP = -20 + 4 = -16

Price elasticity, E = (P/Q)*(dQ/dP)

E = (4/48)*-16 = -4/3