Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 35

A monopolist faces a market demand curve given by
Q = 70 - P
The monopolist's marginal revenue function is given by
MR = 70 - 2Q
a. If the monopolist can produce at constant average and marginal costs of AC = MC =6, what out put level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits?
b. Assume instead that the monopolist has a cost structure where total costs are described by
TC = 0.25Q 2 - 5Q + 300
and marginal cost is given by
MC = 0.5Q - 5.
With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be?
c. Assume now that a third cost structure explains the monopolist's position, with total costs given by
TC = 0.01Q 3 - Q 2 + 45Q + 100
and marginal costs given by
MC = 0.03Q 2 - 2Q + 45
Again, calculate the monopolist's price-quantity combination that maximizes profits. What will profits be? (Hint: set MC = MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.)d. Graph the market demand curve, the MR curve, and the three marginal cost curves from part a, part b, and part c. Notice that the monopolist's profit-making ability is constrained by (1) the market demand curve it faces (along with its associated MR curve), and (2) the cost structure underlying its production.