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?
Answer
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

Expert's answer

The profit maximizing number of rides is where MR = MC = TC' = 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' = 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

So, the right answer is:

Q = 18, P = $64, Π = $660

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' = 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

So, the right answer is:

Q = 18, P = $64, Π = $660

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