12.10. Uncertainty and policy. (Brainard, 1967.) Suppose output is given by y = x + ( + a:)z + u, where z is some policy instrument controlled by the government and & is the expected value of the multiplier for that instrument. Ex and u are independent, mean-zero disturbances that are unknown when the policy-maker chooses z, and that have variances of and ou. Finally, x is a disturbance that is known when z is chosen. The policymaker wants to minimize E [( y*)~] (a) Find E [(v - y*)-] as a function of x, k, y*, of, and on. (b) Find the first-order condition for z, and solve for z. (c) How, if at all, does of affect how policy should respond to shocks (that is, to the realized value of x)? Thus, how does uncertainty about the state of the economy affect the case for "fine-tuning"? (d) How, if at all, does of affect how policy should respond to shocks (that is, to the realized value of x)? Thus, how does uncertainty about the effects of policy affect the case for "fine-tuning"