Question

Consider the following total cost function for an individual firm: C(q) = 10+ q + (1/4)q^2...

Consider the following total cost function for an individual firm:
C(q) = 10+ q + (1/4)q^2
The industry demand is estimated to be:
Q = 100 - P

1) Now suppose there is a monopolist facing the industry demand. Write down the monopolist's pro t function.

2) What is the equation of the monopolists marginal revenue function? Also, explain how the monopolist's marginal revenue function differs from the marginal revenue function of a firm in a long-run perfectly competitive market.

3) What are the monopoly equilibrium levels of price and output?

4) If instead of maximizing profit, the firm wanted to maximize revenue, what price would it set?

5) Numerically verify that the inverse elasticity rule of monopoly pricing, i.e. (P-MC)/P = 1/|ed| is correct in this particular equilibrium

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