The profit of a firm depends on the effort of its Manager (the agent) which the firms Owner (the principal) cannot observe. Independent of the Managers effort, the firms profit depends on future demand conditions as follows (the number in parenthesis is the probability of that demand scenario being realized):
Low Demand (0.3) High Demand (0.3) Medium Demand (0.4) $10 million $12 million Low effort High effort $5 million $7 million $15 million $ 17 million The Manager has the following utility function, where 100 is the Manager's dis-utility of effort, and Wealth represents the Manager's income for working for this firm: Utility (Wealth)0.5 if effort is low or Utility (Wealth)0.5 100 if effort is high The Owner is interested in maximizing the expected profit of the firm (after deduction of the Manager's compensation). The Owner considers three different compensation packages for the Manager: Compensation Package 1: A fixed salary of $575,000. Compensation Package 2: A payment of 6% of profit. Compensation Package 3: A fixed payment of $500,000 plus half of any profit in excess of $15 million. . a. What is the firm's expected profit for each level of the Manager's effort? b. For each offered Compensation Package, please answer these two questions: 1). What effort level will the Manager select? (Explain why in terms of the Manager's utility), and 2). What will be the firm's expected profit? Low Demand (0.3) High Demand (0.3) Medium Demand (0.4) $10 million $12 million Low effort High effort $5 million $7 million $15 million $ 17 million The Manager has the following utility function, where 100 is the Manager's dis-utility of effort, and Wealth represents the Manager's income for working for this firm: Utility (Wealth)0.5 if effort is low or Utility (Wealth)0.5 100 if effort is high The Owner is interested in maximizing the expected profit of the firm (after deduction of the Manager's compensation). The Owner considers three different compensation packages for the Manager: Compensation Package 1: A fixed salary of $575,000. Compensation Package 2: A payment of 6% of profit. Compensation Package 3: A fixed payment of $500,000 plus half of any profit in excess of $15 million. . a. What is the firm's expected profit for each level of the Manager's effort? b. For each offered Compensation Package, please answer these two questions: 1). What effort level will the Manager select? (Explain why in terms of the Manager's utility), and 2). What will be the firm's expected profit
