# Monopoly and Investment under Uncertainty

Suppose a software company is considering developing a new product. Writing the program would cost \$20 million, which would have to be paid immediately. Once written, however, the marginal cost of producing copies of the program would be zero. The firm would be a monopolist in the market for this particular product for 10 years and would face a linear demand curve of the form P = a – bQ in each year. After 10 years the product would be obsolete and demand would drop to zero. Also, you may assume that the product takes one year to develop: if the firm goes ahead, it will be ready for sale beginning in year 1. The interest rate is 5%.

Suppose that based on similar products the firm knows that b is 1/500 but it is not sure about a. It knows that the product will either be a hit or flop. If it is a hit, a will be 300; if it is a flop, a will be 100. If the product has a 15% chance of being a hit, should the firm go ahead with it? You may assume the firm is risk-neutral. Be sure to show all your work, including appropriate decision trees and cash-flow diagrams.

## Solution

URL: https://wilcoxen.maxwell.insightworks.com/pages/362.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 08/18/2016