Question 4 In this problem, we'll study what happens in the basic principalagent model if the principal is restricted in terms of the xed payment 1' participation fee that can be charged. The model is essentially identical to that of lecture 1b. The agent's and principal's payoffs are 1 H=LU-82, 2 ir=xw. Output equals the agent's effort, x = e. The agent has zero outside option, 3 = 0. The timing of the model is as usual: step 1. Principal offers agent an incentive scheme of the form to = or + x. step 2. Agent may accept or reject the offer. If he rejects, he receives his outside option 2 = 0 (and the principal receives ' = 0). step 3. Ifagent accepts, then he chooses e. step 4. Principal pays agent to = or + 3x. We rst remind ourselves of the result from the basic model, where there are no restrictions on what participation fee the principal can charge. a) Work out the agent's payoffmaximizing choice of e' (as a function of 3) in step 3, and the principal's payo' maximizing choice ofoc' and [3' in step 1. You should verify that of = %. For the rest of this question, we'll consider the optimal incentive scheme if the principal is restricted to choose at to be equal to an amount g xed by law, a: = g. Assume that g 2 %. We will guide you through the calculations stepbystep. b) Given that the principal is required to set a: = g: suppose (only for this part (b)} that the agent is always forced to accept the principal's oifer in step 2. Under this assumption, what would the principal's payoEmaximizing choice of K be in step 1? c) Given that the principal is required to set a = Q, what range of incentive strengths [3 would the agent be willing to accept in step 2? (Your answer should be given in terms of a range of values, e.g., a 5 5 b, and should depend on g.) (1) Given that the principal is required to set at = g, what range of incentive strengths 13 would the principal be willing to offer the agent in step 2? Remember that the principal would rather not o'er the agent a contract if it would result in the principal obtaining a negative payo 71'