1. The profits of a firm depend on market condition and on the effort of its man
ID: 1133709 • Letter: 1
Question
1. The profits of a firm depend on market condition and on the effort of its manager Low demand High demand 0.4 100.000 200.000 Probability 0.6 High effort Low effort 100.000 For the manager high effort has a cost of 10.000, while low etfort has no cost Firm has to choose one of the following two wage schemes: a) Flat wage of 20.000 b) Flat wage of 10.000 plus 30% of the profits above 100.000. Manager is risk indifferent. a. From the point of view of the firm, which is the best option? b. From the point of view of the manager, which is the best option?Explanation / Answer
It is given that the probability of low demand is 0.6 and that of high demand is 0.4.
a) The expected profits for the firm when the manager is high effort is given by,
E(Ph) = 0.6*100 + 0.4*200 = 60 + 80 = 140
Expected profits when the manager is low effort,
E(Pl) = 0.6*100 + 0.4*100 = 100
The firm does not know whether the manager is high effort or low effort. If it keeps a flat wage of 20, the manager has no incentives to put effort as he gets the same wage whether he puts high or low effort. So, the profits will also be fixed at 100-20 = 80 since a rational manager will not put high effort.
However, if the wage is fixed at 10 + (30% of the profits above 100), the profits will be100-10 = 90 if the manager puts low effort but if the manager puts high effort the profits of the firm will be 200-30% of (200-100) -10= 160 with a probability 0.4 and 100 with a probability 0.6. This gives us an expected probability of (0.4*160) + (0.6*100) = .124. In either case, the firm has higher profits than when there is a fixed wage. Therefore, the firm will benefit having a performance based wage rather than a fixed wage.
b) Since the manager is indifferent about the risk neutral, he is only concerned about the expected return from being high or low performing.
Expected return if the wage is fixed is 20. Since it costs him 10 for being high performing he chooses to be low performing and earns 20.
Expected return if the wage is 10 + 30% of (Earnings above 100)
In case of flexible wages, he earns 10 if he is low performing and (40-10) =30 if he is high performing and the demand is high.
Here, the expected wage is 0.4* 30 + 0.6*10 = 6 + 12 = 18
Since, the expected return is higher (20) in the fixed wage case and is lower (18) in the flexible wage case, the former is best for the manager even if he is risk indifferent.
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