4. Suppose you own a taxi company in New York City. Assume further the taxi indu
ID: 1103969 • Letter: 4
Question
4. Suppose you own a taxi company in New York City. Assume further the taxi industry in Further, the cost structure NYC is described by a perfectly competitive market structure. your firm faces is described by the following equation: TC-40 6Q+Q where Q = the number of taxi trips. The market price you face P-S36/trip. Note in this problem the taxi company takes the Price, P, as given information. They can sell all the trips they want to at P- S30. Thus, for each additional trip the change in revenues is $36 or the price. That is P = MR. Remember TR = P*Q and Profit = -TR-TC. Note that the profit maximizing rule is find the Q at which MR-MC where MR-d'TR/dQ and MC-dTCdQ. a. What is the profit maximizing or loss minimizing number of trips, Q? Hint the profit maximizing output is where MR MC. b. What is the Economic profit or loss you are making? c. What output level is the minimum point for Average Total Costs (ATC)? d. What output level, Q, and price/trip, P, will economic profits be zero? Note Economic Profits are zero [ie. (Econ = 0) when P ATC.Explanation / Answer
TC = 40 + 6Q + Q2
(a) MC = dTC / dQ = 6 + 2Q
Equating MR (= P) with MC,
36 = 6 + 2Q
2Q = 30
Q = 15
P = $36
(b) When Q = 15,
TR ($) = P x Q = 36 x 15 = 540
TC ($)= 40 + (6 x 15) + (15 x 15) = 40 + 90 + 225 = 355
Profit ($) = TR - TC = 540 - 355 = 185
(c) ATC = TC / Q = (40 / Q) + 6 + Q
ATC is minimized when dATC / dQ = 0
(- 40 / Q2) + 1 = 0
40 / Q2 = 1
Q2 = 40
Q = 6.32
(d) Setting P = ATC,
(40 / Q) + 6 + Q = 36
(40 / Q) + Q = 30
40 + Q2 = 30Q
Q2 - 30Q + 40 = 0
Solving this quadratic equation using online solver,
Q = 28.6 or Q = 1.40
When Q = 28.6, Price = ATC = (40 / 28.6) + 6 + 28.6 = 1.68 + 34.6 = 36.28
When Q = 1.4, Price = ATC = (40 / 1.4) + 6 + 1.4 = 28.57 + 7.4 = 35.97
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.