Consider a manager and a worker. The worker chooses between low effort, which is costless, and high effort, which costs e > 0. There are two states of the world: the "bad" state occurs with probability two-thirds, and the "good" state with probability one-third. If the worker chooses low effort, then the "bad" state yields the manager a payoff of 0, and the "good" state a payoff of 100. If the worker chooses high effort, then the "bad" state yields the manager a payoff of 100, and the "good" state a payoff of 1000. a. (2 pts) Assume the worker does not earn a wage and chooses low effort. What is the expected payoff of the manager? b. (4 pts) Suppose the manager wants to incentivize high effort with the following wage structure: If the payoff is zero, then the worker earns a wage of zero; If the payoff is greater than or equal to 100, then the worker earns a wage of X > 0. Under this wage structure, what is the minimum amount the owner has to pay the employee for high effort? Finally, at this wage, what would be the expected payoff to the manager