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A risk neutral principal hires a risk averse agent to work on a project. The agent's utility function is V(wei) = (w - glei), where w is wage, g(ei) is the disutility associated with the effort level ei exerted on the project. The agent can choose one of two possible effort levels, eH or el, with associated disutility levels g(eH) = 4, and g(el) = 2. . If the agent chooses effort level eh, the project yields 80 with probability 1/2, and 0 with probability 1/2. . If the agent chooses el, the project yields 80 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. Let (wH, wL) be an output-contingent wage contract, where wH is the wage paid if the project yields 80, and wL is the wage if the yield is 0. The agent receives a fixed wage if wH = wL. (a) If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [5 marks] (b) Suppose effort is not observable. What is the optimal contract that the principal should offer the agent? What effort level does this contract implement? [8 marks] (c) Compare the optimal contract in part (a) with that in part (b) and provide intuition for any similarity or difference in the income risk they impose on the agent and in the principal's payoff.Assume that there are no positive externalities to homeownership. Then the household's demand for housing (in square feet) is the marginal social benefit and is a function of the price of housing (in dollars): QD(P) = 2500 - 1000 . P The marginal social cost of housing is constant at $1. a. Draw a graph showing the (inverse) housing demand curve and the marginal social cost curve. b. What is the socially efficient quantity of housing? c. The mortgage subsidy deducts housing expenditure from taxable income. If the marginal tax rate for the household is 30%, what is the net cost to the household for $1 of housing? Add this curve to the graph you drew in part (a). d. How many square feet of housing will the household consume in the presence of the mortgage subsidy? e. What is the deadweight loss caused by the household's consumption choice with the mortgage subsidy