March 27, 2017

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1. Consider a pure monopolist with short-run total cost function given by
STC = 1000 +200 Q + 12.5 Q2. Suppose also that this firm faces an inverse market demand function given by P = 800 – 20 Q.
a. How much should this firm produce and what price should it charge in order to maximize profits?
b. How much economic profit (or loss) would this firm earn?
c. What is the value of this firm’s demand elasticity at its profit-maximizing price?
d. What is the Lerner Index for this firm? LI = -1/ Ed = 0.30

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    2. A monopolist has two plants, A and B, with respective marginal cost functions given by MCA = 10 +QA and MCB = 10 + 2QB. It faces a demand curve given by P = 70 – 1/6 Q.
    a. What is the expression for this firm’s marginal cost function?
    b. How much will this firm produce in order to maximize profit?
    → MC = MR
    c. What price will it charge at that quantity?
    d. How much output should be produced in the two respective plants

    3. A pure monopsonist faces a market supply curve given by the expression P = 10 + Q. The marginal value curve for the input is given by MV = 60 – ½ Q.
    a. Find how much this optimizing monopsonist will purchase of the input.
    b. What price will it pay for the input?

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