A monopolistic pro sports franchise called the Reno Wranglers faces ticket deman
ID: 1111084 • Letter: A
Question
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-162-002Q, 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. 1. 0 a. If the Reno Wranglers are profit maximizers, how many tickets will the franchise 2 sell per unit of time? What price per ticket will the Wranglers charge? he 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 b. 0 much economic profit (or loss) will the franchise earn per unit of time? c. Calculate the vertical intercept of the demand function and the marginal revenue function, and demonstrate that they are equal. In light of the results from parts a and c, calculate the level of consumer surplus associated with the Wranglers. [Hint: Think about the area of a key triangle.] d. 8 If Reno government officials awarded the Wranglers a subsidy of $40,000 per 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 e. 2 Wranglers to stay in town, or would they want them to move? Explain.Explanation / Answer
(a) Profit is maximized by equating MR with MC.
162 - 0.02Q = 66 + 0.01Q
0.03Q = 96
Q = 3,200
From demand function:
3,200 = 16,200 - 100P
100P = 16,200 - 3,200 = 13,000
P = $130
(b) Profit = Total revenue (TR) - Total cost (TC)
TR ($) = P x Q = 130 x 3,200 = 416,000
TC ($) = 206,600 + (66 x 3,200) + (0.005 x 3,200 x 3,200) = 206,600 + 211,200 + 51,200 = 469,000
Profit ($) = 416,000 - 469,000 = - 53,000
Wranglers is making a loss.
(c)
From demand function, When Q = 0, P = 16,200 / 100 = $162 (Vertical intercept, demand curve)
From MR function, When Q = 0, P = $162 (Vertical intercept, MR curve)
Therefore vertical intercept of Demand and MR curves are equal.
(d)
Vertical intercept of demand curve = 162
Consumer surplus = Area between demand curve and equilibrium price
= (1/2) x $(162 - 130) x 3,200 = (1/2) x $32 x 3,200
= $51,200
NOTE: As per Chegg answering guideline, first 4 parts are answered.
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