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Answer to Question #33473 in Microeconomics for Susan

Question #33473
Yellow Cab Co. has a monopoly on taxi services from the Honolulu Airport to Waikiki. The daily demand for taxi services on this rout is given by the demand function Q = 50 – 0.5P. Yellow Cab’s daily costs are TC = 150 + 10Q + 0.5Q^2. What is the profit maximizing number of rides Yellow cab should provide, what price should they charge, and how much profit will they earn?
a.
Q = 25, P = \$50, Π = \$1,250
b.
Q = 25, P = \$50, Π = \$677.50
c.
Q = 18, P = \$64, Π = \$660
d.
Q = 18, P = \$64, Π = \$1,152
The profit maximizing number of rides is where MR = MC = TC&#039; = Q + 10
The profit maximizing can be found in the point on the demand curve with the optimal number of rides.
TR = P*Q = (100 - 2Q)*Q = 100Q - 2Q^2
MR = TR&#039; = 100 - 4Q
100 - 4Q = Q + 10
5Q = 90
Q = 18
P = 100 - 2Q = 64
TP = TR - TC = P*Q - TC = 64*18 - (150 + 10*18 + 0.5*18^2) = 1152 - 492 = 660
Q = 18, P = \$64, &Pi; = \$660

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