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Suppose an entrepreneur owns a firm that has a production technology that generates the following revenue: R(e) = e2+100e where revenue depends on his effort level e. The monetary cost of effort is given by: C(e)= 2e2 The entrepreneuer is risk neutral and maximixes his expected utility.
(a) What is the maximal value (profit) of the firm?
(b) Suppose the entrepreneur sells 100% equity. After selling the firm, what effort level does the entrepreneur choose? What is the value of the firm?
(c) Suppose the entrepreneur sells β% equity. What effort level does the entrepreneur choose? Is it efficient?
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Math solution
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