EX-4

For parts (a) and (b) assume that the monopolist's marginal cost is positive at all levels of output.

When a monopolist operates in the inelastic region of the market demand curve, it can always increase profit by producing less output. Is this statement true or false? Explain.

When a monopolist operates in the elastic region of the market demand curve, it can always increase profit by producing more output. Is this statement true or false? Explain.

Suppose Microsoft has a monopoly in the market for operating systems in Mexico. During 2006 it faces the market demand curve $P = 100 - 10Q$, where $Q$ represents millions of operating systems sold per year.

Suppose you know nothing about Microsoft's production costs. Assuming Microsoft behaves as a profit-maximizing monopolist, an economist predicts that the firm would never sell more than 5 million operating systems in Mexico in 2006. Is this prediction correct or incorrect? Justify your answer.

Calculate the Lerner Index for a monopolistic firm when: $MC = c$, and the price elasticity of demand is $|e| = 2$.

The owner of the Los Angeles Dodgers commissioned a study showing that the demand for stadium seats (per game) is: $P = 40 - 0.5Q$, where $P$ is the average ticket price (in dollars) and $Q$ is the number of seats sold (in thousands). Dodger Stadium has a maximum capacity of 56,000 seats per game. The current ticket price is $10 per seat.

(For simplicity, assume that all seats are identical. In reality, the same analysis could be applied separately to each seating category.)

How much revenue does the owner earn at the current ticket price?

Suppose the owner's primary objective is to maximize revenue. At the current price, are tickets overpriced or underpriced?

The owner offers you 10% of any increase in revenue you can generate during the coming season. Assuming that the only decision variable is the ticket price, how much could you expect to earn per game?

From the owner's perspective, is there an optimal number of empty seats per game? If so, what is that number?

A firm's marginal cost is given by: $MC = 50 + 10q$. The demand curve faced by the firm is: $P = 1300 - 5q$.

Find the profit-maximizing price and quantity.

Suppose the government imposes a lump-sum tax of 5,000, which must be paid as long as the firm produces a positive level of output (the tax is zero if the firm produces nothing). What is the new profit-maximizing price and quantity?

Instead of the lump-sum tax, suppose the government imposes a per-unit tax of 300. What is the new profit-maximizing price and quantity?