Business Calculus Question

Question

Given the demand equation, P= 8700/q^2

find the point elasticity when q=20

Answer 1

price elasticity of demand = percentage change in quantity divided by percentage change in price. when the changes approache zero, it's point elasticity

P =8700/q^2

P'(q) = the derivative of P with respect to q

dP/dq = -17400/q^3

Elasticity = dq/dP = dq/q/dp/p = dq/dp times P/Q

when Q=20, P = 8700/400 = 87/4

P/Q = 87/4/20 = 87/80

dP/dq = -17400/8000 = -174/80 = -87/40

dq/dP = -40/87)

dq/dP times P/Q = (-40/87)(87/4) = -10

Elasticity = -10, although the negative sign is usually dropped, as price elasticity of demand is virtually always understood to be negative, so

Point price elasticity of demand = 10 when q=20