1. Exercise 4 from Chapter 5 in Zhy (page 93)
2. Exercise 3 and 5 from Chapter 6 in Zhy (pages 128-129)
3. Two firms have technologies for producing identical paper clips. Assume that all paper clips are sold in boxes containing 100 paper clips. Firm A can produce each box at unit cost of cA = $6 whereas firm B (less efficient) at a unit cost of cB = $8.
a. Suppose that the aggregate market demand for boxes of paper clips is p = 12 – Q/2, where p is the price per box and Q is the number of boxes sold. Solve for the Nash-Bertrand equilibrium prices pb A and pb B, and the equilibrium profits ∏A b and ∏B b .
4. Historically, most of the diamond mines in the world have been controlled by a few companies and governments. Through clever marketing by diamond producers, many consumers have furthermore become convinced that “diamonds are a girl’s best friend” because “diamonds are forever.” Suppose that the demand for diamond is given by p=90- x and suppose further that the monopolist’s marginal cost curve is given by MC=x
a) Derive the equation for the marginal revenue curve
b) What is the profit-maximizing output level xM? What is the profit-maximizing price pM (assuming that the monopolist can only charge a single per-unit price to all consumers)?
c) In absence of recurring fixed costs, what is the monopolist’s profit?
d) What is the consumer surplus and deadweight loss (assuming that demand is equal to marginal willingness to pay)?
e) What is the cost function if recurring fixed costs are sufficiently high to cause the monopolist’s profit to be zero?