1. A monopolistic pro sports franchise called the Reno Wranglers faces ticket de
ID: 1112425 • Letter: 1
Question
1. A monopolistic pro sports franchise called the Reno Wranglers faces ticket demand that varies according to the equation Q 16200-100P and earns marginal revenue according to the function MR = 162-0.02Q, where Q is the number of tickets (arena seats) sold per unit of time and P is the price per ticket in dollars. The Wranglers incur marginal costs according to the function MC = 66 + 0.01Q. If the Reno Wranglers are profit maximizers, how many tickets will the franchise sell per unit of time? What price per ticket will the Wranglers charge? a. The Reno Wranglers incur total costs according to the function TC = 206,600 + 66Q+0.005Q2. If the Wranglers operate at the profit-maximization point, how much economic profit (or loss) will the franchise earn per unit of time? b, c. Calculate the vertical intercept of the demand function and the marginal revenue d. In light of the results from parts a and c, calculate the level of consumer surplus e. If Reno government officials awarded the Wranglers a subsidy of $40,000 per function, and demonstrate that they are equal. associated with the Wranglers. [Hint: Think about the area of a key triangle.] unit of time, would the Wranglers earn positive economic profit, break even, or earn economic losses? Explain. After this subsidy, would fans still want the Wranglers to stay in town, or would they want them to move? Explain.Explanation / Answer
(a) Profit is maximized when MR equals MC.
162 - 0.02Q = 66 + 0.01Q
0.03Q = 96
Q = 3200
Substituting value of Q in demand function,
3200 = 16200 - 100P
100P = 16200 - 3200 = 13000
P = $130
(b) Profit = Total revenue (TR) - Total cost (TC)
TR ($) = P x Q = 130 x 3200 = 416,000
TC ($) = 206,600 + (66 x 3200) + 0.005 x (3200)2 = 206,600 + 211,200 + 51,200 = 469,000
Profit ($) = TR - TC = 416,000 - 469,000 = - 53,000
Wranglers is making a loss.
(c)
From demand function we get, When Q = 0, P = 16,200 / 100 = $162 (Vertical intercept of the demand curve)
From MR function we get, When Q = 0, P = $162 (Vertical intercept of the MR curve)
So, the vertical intercept of Demand and MR curves are identical (= $162).
(d)
Vertical intercept of demand curve = 162
Consumer surplus (CS) = Area between demand curve and market price
= (1/2) x $(162 - 130) x 3200
= (1/2) x $32 x 3200
= $51,200
(e)
The subsidy is a fixed amount which will not impact MC, therefore loss-minimizing price and output combination will remain unchanged at $130 and 3200 units respectively. However, the subsidy of $40,000 will decrease loss by $40,000 and new amount of loss will be $13,000 (= $53,000 previous loss - $40,000 subsidy).
After subsidy, decision to stay in town or leave will be a decision by Wrangers and not by its fans, since the subsidy will lower the loss for the Wrangers without affective its consumers (fans) who would need to pay the same ticket price as before.
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