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IV. Ralph's Responsibility Center 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[revenuelH] = 4.5, and E[cost*revenuelH] = 4.99. cost;revenue input H input L 1;4 0.49 0.15 1;5 0.41 0.15 2;4 0.01 0.35 2;5 0.09 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)? IV. Ralph's Responsibility Center 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[revenuelH] = 4.5, and E[cost*revenuelH] = 4.99. cost;revenue input H input L 1;4 0.49 0.15 1;5 0.41 0.15 2;4 0.01 0.35 2;5 0.09 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)