3 ■3.19. COMPETITIVE PRESSURE. Suppose that a firm's profits are given by π = a + (e) + e, where a denotes the intensity of product market competition, e effort by the manager, and e a random shock. The function (e) is increasing and concave, that is, do/de>0 and d² /de² <0. qua In order for the firm to survive, profits must be greater than 7. The manager's payoff is ß>0 if the firm survives and zero if it is liquidated, that is, if profits fall short of the minimum target. The idea is that if the firm is liquidated, then the manager loses his or her job and the rents associated with it. ad arsolbad Suppose that is normally distributed with mean μ and variance o², and that >T. Show that increased product market competition (lower a) induces greater effort by the manager, that is, de/da <0.

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