Problem 1

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.

What are your profits if you do not make the investment?

What are your profits if you do make the investment?

Instruction: Do not include the investment of $200 as part of your profit calculation.

Should you invest the $200?

Problem 2

You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell high-powered computers to businesses. From the two businesses' perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P = 5,900 - Q and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How much will this process improve BlackSpot's profits?

(Hint: Consider solving for the duopoly outcome before and after the change in BlackSpot's marginal costs.)