1. Paul is planning to hire Alicia for a project. Both are risk neutral with linear utility functions. Paul's utility function is: Uz = R-W, where R is revenue and W the wage rate. Alicia's utility function is: U2 = W-e, where e is the level of effort. Alicia may put in a high effort, ex or a low effort, e_. Paul's revenue can be high RH = 20 or low RL = 10. If Alicia puts in a high effort (low effort) there is a 90% (10%) probability that revenue will be high and a 10% (90%) probability that revenue will be low. Assume that ex = 8 and e. = 2. However, they are not observable by Paul. Since the efforts are not observed, the wages offered by Paul do not depend on efforts, but they depend on the levels of revenue. If the revenue is high Alicia receives W. and if the revenue is low Alicia receives W. where WH > W. Assume there is no bonus. If a contract is rejected payoffs are (0,0). Draw the game tree. Write and explain the incentive compatibility constraint and the participation constraint. Draw the graphs of the two constraints maintaining them as inequalities. For the graph measure W along the horizontal axis and W. along the vertical axis. Determine the wages under the optimal contract. (the optimal contract will specify the two wages that will satisfy the above constraints). Show the optimal contract (the wage combinations) on the above graph. 1. Paul is planning to hire Alicia for a project. Both are risk neutral with linear utility functions. Paul's utility function is: Uz = R-W, where R is revenue and W the wage rate. Alicia's utility function is: U2 = W-e, where e is the level of effort. Alicia may put in a high effort, ex or a low effort, e_. Paul's revenue can be high RH = 20 or low RL = 10. If Alicia puts in a high effort (low effort) there is a 90% (10%) probability that revenue will be high and a 10% (90%) probability that revenue will be low. Assume that ex = 8 and e. = 2. However, they are not observable by Paul. Since the efforts are not observed, the wages offered by Paul do not depend on efforts, but they depend on the levels of revenue. If the revenue is high Alicia receives W. and if the revenue is low Alicia receives W. where WH > W. Assume there is no bonus. If a contract is rejected payoffs are (0,0). Draw the game tree. Write and explain the incentive compatibility constraint and the participation constraint. Draw the graphs of the two constraints maintaining them as inequalities. For the graph measure W along the horizontal axis and W. along the vertical axis. Determine the wages under the optimal contract. (the optimal contract will specify the two wages that will satisfy the above constraints). Show the optimal contract (the wage combinations) on the above graph