Question

Suppose a monopolist producing in a market faces the inverse demand curve p=250− 5q and has the cost function C(q)= 100−2q+(q−5)² - What is the profit maximizing price and quantity? - What is the market power of this firm using the Lerner Index at this output?

Answer 1

The profit-maximizing price for the monopolist is $800 and the quantity is 5 units.

Step-by-step explanation:

The profit maximizing price and quantity for a monopolist producing in a market can be determined by following a three-step process:

1. Step 1: Determine the profit-maximizing level of output: The monopolist selects the quantity where MR (marginal revenue) equals MC (marginal cost), which in this case is 5 units.
2. Step 2: Decide what price to charge: The monopolist draws a line straight up from the profit-maximizing quantity to the demand curve to find the corresponding price, which in this case is $800.
3. Step 3: Calculate total revenue, total cost, and profit: Total revenue is found by multiplying the quantity sold by the price, which gives $4,000. Total cost is found by multiplying the quantity sold by the average cost, which gives $1,650. Subtracting total cost from total revenue gives a profit of $2,350.

Hence, the profit-maximizing price is $800 and the quantity is 5 units.