2. A restaurant is either profitable (with profit of $10,000) or unprofitable (with zero profits) and the outcome of profits is observable to the owner of the restaurant. The owner hires a manager to run the restaurant. The manager can choose high (H) or low effort (L) into running the restaurant. High effort costs more to the manager than low effort. age 1 of 4 The restaurant's success in making $10,000 in profits depends on the manager's effort but is not completely determined by it. So even if the manager puts in high effort it is possible for the restaurant to make zero profits and conversely positive profits can be realized even if the manager puts in low effort. However, the probability of making high profits (p) is higher when the manager puts in high effort than when he puts in low effort. The following table describes the probability of success, p and effort costs, C for each type of effort p C High Effort, H 0.8 $200 Low Effort, L 0.4 $0 The manager is risk-neutral; will accept a wage contract as long as his expected surplus from the contract is greater than or equal to zero; and exerts high effort as long as his expected employee surplus from high effort is greater than or equal to the expected employee surplus from low effort. . Observable Effort a) Suppose the owner could observe the manager's effort correctly, describe the wage contract that the owner would choose for the manager. b) What effort level will the manager choose under this wage contract? c) What is the restaurant owner's expected profit, the manager's expected surplus and the expected total surplus under this fixed wage contract? Fill in the table. Expected Profit Expected Employee Surplus Expected Total Surplus d) is the outcome efficient? Unobservable Effort Now suppose the owner cannot observe effort. e) If the owner continued to offer the wage contract in part a), what effort level would the manager choose? What are the expected profits to the restaurant with this wage contract? Suppose the wage contract was contingent on profits that are realized after the manager has exerted effort. Page 2 of 4 f) Describe the participation constraint that this contract should satisfy to make the manager accept the employment offer. g) What is the incentive constraint that will induce the manager to exert high effort? h) Suppose the firm sets the low wage equal to zero, i.e.w" = $0, what is the profit maximizing high wage that will induce the manager to exert high effort? i) Does the wage contract obtained in part h) satisfy the participation constraint? j) What are the expected profits to the firm, the expected employee surplus to the manager and the expected total surplus under the optimal variable wage contract? Fill in the table and compare it to the expected profits, employee surplus and total surplus obtained in partc). Expected Profit Expected Employee Surplus Expected Total Surplus 2. A restaurant is either profitable (with profit of $10,000) or unprofitable (with zero profits) and the outcome of profits is observable to the owner of the restaurant. The owner hires a manager to run the restaurant. The manager can choose high (H) or low effort (L) into running the restaurant. High effort costs more to the manager than low effort. age 1 of 4 The restaurant's success in making $10,000 in profits depends on the manager's effort but is not completely determined by it. So even if the manager puts in high effort it is possible for the restaurant to make zero profits and conversely positive profits can be realized even if the manager puts in low effort. However, the probability of making high profits (p) is higher when the manager puts in high effort than when he puts in low effort. The following table describes the probability of success, p and effort costs, C for each type of effort p C High Effort, H 0.8 $200 Low Effort, L 0.4 $0 The manager is risk-neutral; will accept a wage contract as long as his expected surplus from the contract is greater than or equal to zero; and exerts high effort as long as his expected employee surplus from high effort is greater than or equal to the expected employee surplus from low effort. . Observable Effort a) Suppose the owner could observe the manager's effort correctly, describe the wage contract that the owner would choose for the manager. b) What effort level will the manager choose under this wage contract? c) What is the restaurant owner's expected profit, the manager's expected surplus and the expected total surplus under this fixed wage contract? Fill in the table. Expected Profit Expected Employee Surplus Expected Total Surplus d) is the outcome efficient? Unobservable Effort Now suppose the owner cannot observe effort. e) If the owner continued to offer the wage contract in part a), what effort level would the manager choose? What are the expected profits to the restaurant with this wage contract? Suppose the wage contract was contingent on profits that are realized after the manager has exerted effort. Page 2 of 4 f) Describe the participation constraint that this contract should satisfy to make the manager accept the employment offer. g) What is the incentive constraint that will induce the manager to exert high effort? h) Suppose the firm sets the low wage equal to zero, i.e.w" = $0, what is the profit maximizing high wage that will induce the manager to exert high effort? i) Does the wage contract obtained in part h) satisfy the participation constraint? j) What are the expected profits to the firm, the expected employee surplus to the manager and the expected total surplus under the optimal variable wage contract? Fill in the table and compare it to the expected profits, employee surplus and total surplus obtained in partc). Expected Profit Expected Employee Surplus Expected Total Surplus