Question

2. The dema nd for attendance for a play at the local performing Art Centre is P = 200 -0.04 QD, where P = Price and QD is the quantity of tickets demanded. a. At what Price and quantity does unit elasticity b. occur? What is the maximum revenue possible? c. If the seating capacity was only 2,000, what price would be charged and what is the maximum revenue? d. If the seating capacity was only 1,500, what price would be charged and what is the maximum revenue?

Answer 1

a) P = 200 = 0.04 Q_0 Q_0 = 200 minus p/0.04 = 5000 p/0.04 = elasticity = dQ/dP times P/Q = 1 dQ/dP = 1/0.04 elasticity = minus 1/0.04 times P/Q = 1 = minus p = 0.040 = P/Q = minus 0.04 = minus 4/100 Thus Price & Qty could be any nos with ratio of 4/100 e.g p = 40 Q = 1000 b) P.Q = 2000 minus 0.040^2 TR = 2000 minus 0.040^2 dTR/dQ = 200 minus 0.08 Q ------ (1) d^2 TR/dQ^2 = 0.08 [It is negative thus TR will be maximum] equate equation (1) to 0 200 minus 0.08 Q = 0 Q = 2500 \r\n c) If selecting is 2000 then q = 2000 p = 2000 = 0.04 (2000) = 200 minus 80 p = 120 Revenue (120) (2000) = 200 (2000) minus 0.01/(2000)^2 = 400000 minus 1600000 TR = 2400000