a)You are the owner of a company and need to design a compensation package for the manager of your company. The following table gives you the probabilities of market demand and profit of the firm (Profit is calculated before the compensation of the manager is deducted). You are risk averse, and the manager is risk-neutral with the utility function below:

Market Demand

Low Demand

High Demand

Market Probabilities

0.1x2

?

Low Effort

P = $ 3 million

P = $6 million

High Effort

P = $5 million

P = $9 million

Utility = W^0.5 -5 when making low effort (5 is the utility cost of making low effort)

Utility = W^0.5 - 20, when making high effort (20 is the utility cost of making high effort)

W is the income level of the manager.

The possible compensation packages are:

Package 1: Pay the manager a constant salary of $250,000 per year.

Package 2: Pay the manager 5% of the yearly profits. (No fixed salary, just the 5% of the yearly profit)

a)What level of effort will the manager make under package 1? (Hint: calculate the expected utility of the manager if s/he makes low effort and if s/he makes high effort)

b)What level of effort will the manager make under package 2?

c)What will be expected profit of the firm under package 2?