2. Suppose you are the manager of Alpha Enterprises, a firm that holds a patent that makes it the exclusive manufacturer of bubble memory chips. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for bubble memory chips are Q = 25 - .5P; C = 50 + 2Q.
a. What is the firm's inverse demand function?
b. What is the firm's marginal revenue when producing 4 units of output?
c. What level of output would maximize profits?
d. At what price would you maximizing profits?
e. What will be the dollar level of your profits?
A. Q = 25 - 0.5P --> 0.5P = 25 - Q --> P = 50 - 2Q
B. Revenue = P * Q = (50 - 2Q) * Q = 50Q - 2Q^2
Marginal revenue = 50 - 4Q ...
This solution looks at the inverse demand function, marginal revenue, maximum profits for a firm with a patent (monopolist).