Given the following demand functions find the point elastici

Given the following demand functions find the point elasticity at a price of $4 and indicate if demand is elastic or inelastic at that point (give your answer as a fraction): a. Qd = 360 - 10P^2 b. Qd = 56 - 8P^0.5

Solution

( a)Qd = 360 - 10P^2 (b). Qd = 56 - 8P^0.5

Point elasticity of demand = (-1/slope)(P/Q)

Qd = 200

P = [(360-Qd)10]^0.5

DQ/DP = -20P

Price = $4

         = -80

Point elasticity of demand = (1/80)(4/200)

                                           = .0025

Demand is inelastic since the value of Point elasticity of demand is less than one.

At p = $4, Q = 40

Point elasticity of demand = (-1/slope)(P/Q)

DQ/DP = -4/P^.05

                           P = $4

                           = -2

                Point elasticity of demand = (-1/-2)/(4/40)

                                                            = .05

                Demand is inelastic since the value of Point elasticity of demand is less than one.