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DSME6651 Economics Analytics

Homework #3

1. In the 1960s, tobacco producers engaged in fierce battles for market share. The major weapon in that war was advertising — advertising that was designed not to attract new smokers, but to lure smokers away from competing brands.

Consider the following scenario: There are two tobacco sellers, Phillip and R. J., each of whom can choose to advertise on TV (at a cost of $10 million) or not. If they choose the same business strategy, they will split the market evenly and make $50 million pre-advertising profits each. (The pre-advertising profit is the profit before deducting the costs for advertisement.) If one chooses to advertise while the other does not, the firm which advertises will steal half the other’s customers and capture $80 million of pre-advertising profit; the other will earn $20 million.

a. Assume that two firms only compete once. Write down the normal form of this one-shot game using the information above. (Hint: the payoff for each firm is the post-advertising profit.)

b. What is the Nash equilibrium in this one- shot game? Is the equilibrium outcome a good one for anybody? Suppose that Phillip and R. J. promise one another that they will not advertise. Is such a promise credible?

c. Now suppose that the firms will compete for infinite periods. If the interest rate is 10%, could these firms use trigger strategies to support cooperation? Show the reason.

2. You are the manager of Taurus Technologies, and your sole competitor is Spyder Technologies. The two firms’ products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 4Qi, and the inverse market demand curve for this unique product is given by P = 160 – 2Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $200, Taurus Technologies can bring its product to market before Spyder finalizes production plans. Should you invest the $200? Use calculations to explain.

3. A monopoly is considering selling several units of a homogeneous product as a single package. A typical consumer’s demand for the product is Qd = 50 - 0.25P, and the marginal cost of production is $120.

a. Determine the optimal number of units to put in a package.

b. How much should the firm charge for this package?

4. A manager can adopt only one of three projects – A, B or C. They generate different revenues in different economic conditions – Boom, Norm or Recession. The probability of each condition is – 20% for Boom, 60% for Norm and 20% for Recession. The revenues are listed below.

If the manager is risk-averse and the cost of adopting any project is 100, which project do you think he may adopt? What if the cost is 150?