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Suppose the Calloway Cab Company has an exclusive franchise to provide limousine service between the airport and center city. Its total cost is TC = 2400 + 60Q + .50Q^{2}, where Q is rides per day. Its marginal cost function is MC = 60 + Q (the first derivative of the total cost function). The daily demand function for rides between the two destinations is P = 200 - Q, where P is the fare.
a. On a graph representing the market for limousine service between the airport and center city, plot the market demand curve.
b. Find the equation representing total revenue as a function of Q only.
c. Find the equation for Calloway’s marginal revenue as a function of Q only.
d. Plot the marginal revenue curve on your graph
e. Plot the marginal cost curve on your graph
f. Using algebra, calculate Calloway’s profit maximizing output.
g. What price will it charge?
h. What profit will it earn?
i. Show Calloway's on your graph.