Question

Given the demand function is Q = 180-5P, find the following: a. The revenue function b. The revenue maximizing output and price c. The own-price elasticity ofdem and at P = $80 own-price elasticity of demand (En) is equal to one, in absolute value. What is the nature of total revenue when lepl 1?

Answer 1

Q = 180 - 0.5P Or, P = 360-2Q TR = PQ = 360Q - 2Q^2 TR is maximized at the point MR = 0 MR = d TR/dQ = 360 - 4Q Thus, 360 - 4Q = 0 Or, Q = 360/4 = 90 Thus, P = 360 - 2(90) P = $180 Thus, revenue maximizing P = $180 and Q = 90 units Price elasticity = (dQ/dP)(P/Q) First, compute dQ/dP = -0.5 Also, at P = $80, Q will be 140 units Thus, elasticity = (- 0.5)(80/140) = -0.286 Price elasticity = (dQ/dP)(P/Q) = 1 Or, 0.5(P/Q) = 1 Or, 0.5(P/Q) = 1 Q = 0.5 P---(1) Substitute (1) in demand function equation This gives Q = 180 - 0.5P Or, 0.5P = 180 - 0.5P Or, P = $180 and thus Q = 90 units