1s given by (1) =(a/2)〔T where a. b t The first term, (a/2)(m,), is the cost of inflation. Notice that our use of a quadratic form me ans that these costs rise at an increasing rate with the rate of inflation, t. The second term, b+t -+), is the benefit from inflation shocks. Here, we use a linear form for convenience.e Given that the benefit parameter, b, is positive, an increase in unexpected inflation, Tt -t, reduces costs. We can think of these benefits as reflecting reductions in unemployment or increases in governmental revenue we allow the benefit parameter,bt, to move around over time. For example, a supply shock--which raises the natural rate of unemployment--may increase the value of reducing unemployment through aggressive monetary policy. Alter- natively, a sharp rise in government spending increases the incentives to raise revenue via inflationary finance. In our example, t is distributed randomly with a fixed mean, b, and variance, o 23 (Hence, we neglect serial correlation in the natural unemployment rate, government expenditures, etc. The policymaker's objective at date t entails minimization of the expected present value of costs (2)z=E[z tt where is the discount rate that applies between periods t and t+1. We assume that r+ is generated from a stationary probability distribution (There fore, we again neglect any serial dependence. Also, the discount rate is generated independently of the benefit parameter, bt. For the first period ahead, the distribution of r. implies a distribution for the discount factor,-6- is given by 2 e (1) z = (a/2)(rrt) - bt(Tr — 7rt), where a, bt > 0. The first term, (a/2)(rT)2, is the cost of inflation. Notice that our use of a quadratic form means that these Costs rise at an increasing rate with the rate of inflation, Tr. The second term, bt(lrt - ir), is the benefit from inflation shocks. Here, we use a linear form for convenience.2 Given, that the benefit parameter, bt, is positive, an increase in unexpected inflation, - rr, reduces costs. We can think of these benefits as reflecting reductions in unemployment or increases in governmental revenue. We allow the benefit parameter, bt, to move around over time. For example, a supply shock--which raises the natural rate of unemployment--may increase the value of reducing unemployment through aggressive monetary policy. Alter￾natively, a sharp rise in government spending increases the incentives to raise revenue via inflationary finance. In our example, bt is distributed randomly with a fixed mean, , and variance, a.3 (Hence, we neglect serial correlation in the natural unemployment rate, government expenditures, etc.) The policymaker's objective at date t entails minimization of the expected present value of costs, (2) = E[z + (l+rt+l + r)(l+r+1) Z2 + where r is the discount rate that applies between periods t and t + 1. We assume that r is generated from a stationary probability distribution. (Therefore, we again neglect any serial dependence.) Also, the discount rate is generated independently of the benefit parameter, bt. For the first period ahead, the distribution of r implies a distribution for the discount factor