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Consider a situation in which a risk-neutral principal wishes to contract an agent to work on a project. The project produces output x = e + & where e is the agent's effort and & is a normally distributed random variable with mean 0 and variance 1 (that is, & ~ N(0, 1)). The agent's utility of wealth function is u(w) = E(w) -2Var(w) where E is expectation and Var is variance. The agent's disutility of effort function is v(e) = 0.5e- and his reservation utility is u = 0. The principal can only offer contracts with the form w= a + Bx From this we gather that the agent's expected utility from a contract can be written as a + Be - 28- - 0.5e While the principal's expected utility from a contract can be written as (1 - B)e - a. a) Given the contract w =a + Bx, what effort level will maximize the agent's expected utility? b) Derive the optimal values for a and B for the principal when effort is unverifiable. c) How does the optimal B in the verifiable effort contract differ from the optimal B in the unverifiable effort contract? Discuss the implications for the efficiency of risk sharing and the efficiency of effort in the case of non-verifiable effort. d) Suppose that in addition to observing output x, the principal observes the variable y = e + V where V ~ N(0, 1) is independent of &. If we assume that the principal's payoff does not depend directly on y, should he nevertheless include y in the contract he offers the agent? Why or why not?suppose the firm's cost function is c(q)=4q- + 16 a. find variable cost, fixed cost, average cost, average variable cost and average fixed cost. ( hint: marginal cost is given by Mc =8q) b. show the average cost, marginal cost and average variable cost curves on graph. c. Find the output that minimizes average cost. d. At what range of prices will the firms produce a positive output? e. At what range of prices will the firm earn a positive profit? f. At what range of prices will the firm earna negative profit