Consider the following game, with a risk-neutral principal with preferences = q - w hiring an agent with preferences U = w-e.. The agent's reservation utility is given by U = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: I Probability (q=0) Probability (q=400) 0.6 e=0 e=10 0.1 0.4 0.9 a) Illustrate this game of moral hazard using a fully labeled game t ith payouts. b) Write out the agent's incentive compatibility (ICC) and participation constraints (PC). c) Interpret those constraints in words-what are they imposing on the contract being designed by the principal? d) Find the optimal contract under the assumption that agents compete for principals. Begin by identifying which constraints will bind with equality! e) What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain..