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Problem 12-2. The conditions of this problem are given in Example 9.1 of Avinash K. Dixit's Optimization in Economic Theory: "An owner has to hire a manager to run a project. If a project succeeds, it will produce value V. The probability of success depends on the quality of the manager's work. Given high quality, the project will succeed with probability p, but low quality will reduce this to q. The basic salary needed to attract a manager is w. But he has to exert himself more to achieve high quality, and will do so only if he is paid a premium e. Both the owner and the manager are risk-neutral, that is, each maximizes the mathematical expectation of his mathematical returns (minus the money-equivalent cost of effort in the case of the manager)." 12-2a. If V = $300, p = 50%, q = 41.67% (that's forty one and two-thirds) w $120, and e = $10, is it possible to design a contract that is optimal for both parties, under which the manager works hard? If so what is it, and if not why not