Sunflower Industries has been having problems with the accountability of their m

Question

Sunflower Industries has been having problems with the accountability of their managers not being what it should be. Company performance has been slack lately and Sunflower is gearing up for the hire of a new manager. They, however, need to figure out an appropriate manager compensation contract that will increase accountability of the manager.

If the manager works hard (a1), net income will be one of $200 or $450 (before manager compensation) with the probability of 0.35, 0.65, respectively.If the manager shirks (a2), net income will be one of $200 or $450 with probability 0.75, 0.25 respectively.

The interview with the potential new manager yields that he is rational, risk averse with the utility for money equal to the square root of the amount of money received, and effort averse with the disutility of effort of 2 if he works hard and 0.5 is he shirks. Required:

(a) Offered salary is $50 per period plus 20% of firm profits before manager compensation. Will the manager take a1 or a2?

(b) Instead, offer salary of $0 plus 30% of firm profits before manager compensation. Will the manager take a1 or a2?

(c) Does the manager’s effort decision change between parts (a) and (b)? Why or why not?

Explanation / Answer

Answer:

Payoff Table

                                                            Manager’s Act

                                    A1 (work hard)                       A2 (shirk)

                        Payoff             Probability       Payoff             Probability

High Profit      $450                  0.65             $450                  0.25

Low Profit      $200                  0.35             $200                  0.75

(a)        The manager’s expected utility for each act is:

            EU(a1) = 0.65(50 + 0.2 x 450)1/2 exponent + 0.35(50 + 0.2 x 200)1/2 exponent –2

                        = 0.65 x 11.83 + 0.35 x 9.49 – 2

                        = 7.69 + 3.3215 – 2

                        = 9.01

            EU(a2)= 0.25 x 11.83 + 0.75 x 9.49 – 0.5

                        = 2.9575 + 7.1175 – 0.5

                        = 9.575

            The manager would take a2.

(b)        EU(a1)= 0.65(0.3 x 450)1/2 exponent + 0.35(0.3 x 200)1/2 exponent - 2

                        = 0.65 x 11.62 + 0.35 x 7.75 – 2

                        = 7.55 + 2.7125 – 2

                        = 8.26

            EU(a2)= 0.25 x 11.62 + 0.75 x 7.75 – 0.5

                        = 2.905 + 5.8125 – 0.5

                        = 8.22

Manager would now take a1.

(c)        Yes. The higher profit percentage in part (b) provides sufficiently more incentive that it overcomes the disutility of working hard.

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