Problems

  1. Find marginal revenue for the firms that face the following demand curves:

    1. Q = 1,000 – 5P

    2. Q = 100P–2

  2. Suppose a firm faces demand of Q = 300 – 2P and has a total cost curve of TC = 75Q + Q2.

    1. What is the firm’s marginal revenue?

    2. What is the firm’s marginal cost?

    3. Find the firm’s profit-maximizing quantity where MR = MC.

    4. Find the firm’s profit-maximizing price and profit.

  3. Suppose that American Borax is a monopolist and that the worldwide demand for borax is Q = 100 – P, where Q is tons of borax and P is the price per ton. The total cost function for American Borax is TC = 10Q + 0.5Q2.

    1. Write out the firm’s total revenue as a function of Q.

    2. What is the profit function for American Borax?

    3. Find the firm’s profit-maximizing quantity by applying calculus to the profit function.

    4. Find American Borax’s profit-maximizing price and profit.

  4. Suppose a firm faces the inverse demand curve P = 600Q–0.5. The firm has the total cost curve TC = 1,000 + 0.5Q1.5. Find the firm’s profit-maximizing output, price, and profit.

  5. Consider a firm in a perfectly competitive market with total costs given by

    TC = Q3 – 15Q2 + 100Q + 30

    1. What is this firm’s marginal cost function? Over what range of output are the firm’s marginal costs decreasing? Increasing?

    2. Suppose that the market price is $52. What is this firm’s profit-maximizing level of output? How do you know this is the profit-maximizing output? How much profit does this firm earn by producing the profit-maximizing output?