Organizers of Monster Truck Pull events at B.C. Place estimate the demand for ti
ID: 1216463 • Letter: O
Question
Organizers of Monster Truck Pull events at B.C. Place estimate the demand for tickets to be given by the following equation :
Q x = 100 - 3.0Px + 2.0I – 1.5PY + 0.2A
where Q x = number of tickets sold, in thousands
Px = price of tickets, in dollars
I = personal disposable income, in thousands of dollars per year
PY = price of tickets to WWF wrestling events, in dollars
A = Advertising expenditures for Monster Truck Pull events, in thousands of dollars per year
Currently Px = $40, I = 50, PY = $30, and A = 50.
(a) Calculate the elasticity of demand for tickets to Monster Truck Pull events with respect to (i) its own price, (ii) income, and (iii) the price of tickets to WWF wrestling events.
(b) What price should the organizers charge if they are interested in maximizing revenue.
Because of the beefed up security required (too many “testosterone-tripping mange heads” in one place!), the seating capacity for such events is restricted to 65,000. If the marginal cost of organizing a Monster Truck Pull event is $15.00, how many empty seats per event make sense from the organizer’s point of view? Should the current price be increased or decreased if organizers are primarily interested in maximizing profits.
Explanation / Answer
Qx = 100 - 3Px + 2I - 1.5PY + 0.2A
With given values,
Qx = 100 - 3 x 40 + 2 x 50 - 1.5 x 30 + 0.2 x 50 = 100 - 120 + 100 - 45 + 10
Qx = 45 ('000) = 45,000
(a)
Elasticity for own price = (dQx / dPx) x (Px / Qx) = - 3 x (40 / 45) = - 2.67
Elasticity for income = (dQx / dI) x (I / Qx) = 2 x (50 / 45) = 2.22
Elasticity for WWF tickets = (dQx / dPY) x (PY / Qx) = - 1.5 x (30 / 45) = - 1
(b)
Qx = 100 - 3Px + 2 x 50 - 1.5 x 30 + 0.2 x 50 = 100 - 3Px + 100 - 45 + 10 = 165 - 3Px
3Px = 165 - Qx
Px = 55 - (Qx / 3)
Total revenue, TR = Px. Qx = 55Qx - (Qx2 / 3)
Revenue is maximized when dTRx / dPx = 0
55 - (2Qx / 3) = 0
2Qx / 3 = 55
Qx = 82.5 ('000) = 82,500
Px = 55 - (Qx / 3) = 55 - (82.5 / 3) = 55 - 27.5 = 27.5
(c) Profits are maximized if
dTRx / dQx = MC
55 - (2Qx / 3) = 15
2Qx / 3 = 40
Qx = 60 ('000) = 60,000
So, Optimum number of empty seats = 65,000 - 60,000 = 5,000
(d) Own price elasticity = - 2.67
Since absolute value of elasticity is higher than 1, demand is elastic and so, price should be lowered to increase revenue and increase profits.
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