expectation and all future expectations for i>0 as givens when choosing the current inflation rate The ere tore is chosen to minimize the expected cost for the current period, Ez,, while treating me and all future costs as fixed. Since future costs and expectations are independent of the policymaker's current actions, the discount factor does not enter into the results. The solution from minimizin.r here z is given in eq.(), is a (discretion We use carets to denote the solution under discretion ith other cost Inctions, T+ would depend also on T.) Given rational expectations, people predict inflation by solving out the ker 's opt zation problem and forecasting the solution for t as well as possible. In the present case they can calculate exactly the choice of inflation from eq(3)--hence, the expectations are Since inflation shocks are zero in equilibrium--that is,T the cost from eq(1)ends up depending only on T. In particular, the cost 1 =(1/2)(b)/a (discretion) Policy under a Rule Suppose now that the policymaker can commit himself in advance to a rule for determining inflation. This rule can relate to variables that the policymaker knows at date t. In the present case no one knows the parameters, b. and t date t. But, everyone knows all previ of these parameters. There fore, the policymaker can condition the infla- tion rate, t+, only on variables that are known also to the private agent (The policymaker could randomize his choices, but he turns out not to have-8— expectation, Tr, and all future expectations, ir. for i > 0, as givens when choosing the current inflation rate, Therefore, is chosen to minimize the expected cost for the current period, Ezt, while treating 1T and all future costs as fixed. Since future costs and expectations are independent of the policymaker's current actions, the discount factor does not enter into the results. The solution from minimizing Ez, where z is given in eq. (1), is (3) = /a (discretion) We use carets to denote the solution under discretion. (With other cost functions, ii would depend also on Tr.) Given rational expectations, people predict inflation by solving out the policymaker's optimization problem and forecasting the solution for Trt as well as possible. In the present case they can calculate exactly the choice of inflation from eq.(3)--hence,the expectations are (4) = = Since inflation shocks are zero in equilibrium-that is, the cost from eq. (1) ends up depending only on iT In particular, the cost is A —2 (5) z = (1/2) (b) /a (discretion). Policy under a Rule Suppose now that the policyinaker can conunit himself in advance to a rule for determining inflation. This rule can relate to variables that the policymaker knows at date t. In the present case no one knows the parameters, b and at date t. But, everyone knows all previous values of these parameters. Therefore, the policymaker can condition the infla￾tion rate, only on variables that are known also to the private agents. (The policymaker could randomize his choices, but he turns out not to have