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Ralph is a manager for Alice's firm. Ralph supplies one of two inputs a = H or L, has utility U(w, a) = -exp(-0.0001[w-c(a)]), has personal cost c(H) = 4,000, and c(L) = 0, and his reservation wage is M = 0 (Alice knows Ralph's preferences). Cost and revenues are potential performance measures with the following information structure (joint likelihoods) assigned based on E[cost|L] = 1.7, E[cost]H] = 1.1, E[revenue|H] = 4.5, and E[cost revenue|H] = 4.99. cost revenue 1:4 1:52:42:5 input H 0.49 0.41 0.01 0.09 input L 0.15 0.15 0.35 0.35 LR(rev=4) = 1 LR(rev-5) = 1 LR(cost=1) = 1/3 LR(cost=2) = 7 Required: Recommend to Alice whether Ralph is to be evaluated as the manager of a cost center, revenue center, revenue and cost center, or profit center. Why (hint: consider incentives and risk aversion)?