3.11 A monopoly manufacturing plant currently uses many workers to pack its product into boxes. It can replace these workers with an expensive set of robotic arms. Although the robotic arms raise the monopoly’s fixed cost substantially, they lower its marginal cost because it no longer has to hire as many workers. Buying the robotic arms raises its total cost: The monopoly can’t sell enough boxes to make the machine pay for itself, given the market demand curve. Suppose the incumbent does not invest. If its rival does not enter, it earns $0 and the incumbent earns $900. If the rival enters, it earns

$300 and the incumbent earns $400. Alternatively, the incumbent invests. If the rival does not enter, it earns $0 and the incumbent earns $500. If the rival enters, the rival loses $36 and the incumbent makes $132. Show the game tree. Should the monopoly buy the machine anyway? (Hint: See Solved Problem 14.3.)