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Question 4 In this problem, we'll study what happens in the basic principal-agent model if the principal is restricted in terms of the xed payment / participation fee that can be charged. The model is essentially identical to that of lecture 1b. The agent's and principal's payoffs are 12 u=we, 2 7t=xw. Output equals the agent's effort, x = e. The agent has zero outside option, 2 = O. The timing of the model is as usual: 5th 1. Principal offers agent an incentive scheme of the form to = a + x. 5th 2. Agent may accept or reject the offer. If he rejects, he receives his outside option g = 0 (and the principal receives H = 0). step 3. If agent accepts, then he chooses e. 5th 4. Principal pays agent to = a + Bx. 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 payoff-maximizing choice of 6* (as a function of ) in step 3, and the principal's payoff 1 maximizing choice of as and [5* in step 1. You should verify that (1* = 5. For the rest of this question, we'll consider the optimal incentive scheme if the principal is restricted to choose a to be equal to an amount g xed by law, a = g. Assume that g 2 %. We will guide you through the calculations step-by-step. 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 offer in step 2. Under this assumption, what would the principal's payoff-maximizing choice of g be in step 1? c) Given that the principal is required to set a = g, 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 S [3 s b, and should depend on g.) d) Given that the principal is required to set a = Q, what range of incentive strengths 5 would the principal be Willing to offer the agent in step 2? Remember that the principal would rather not offer the agent a contract if it would result in the principal obtaining a negative payoff, 71'