INTEREST-RATE RULES: Framework for Analysis 4

We can think of as representing variation in the “natural” or “potential” level of output, since it is expected deviations Y — Ys, rather than deviations in the level of output relative to trend, that results in a desire by price-setters to increase the relative price of their goods, which in equilibrium requires inflation of the average level of prices. (An equilibrium in which no prices are ever changed is consistent with (1.18) as long as Yt = Yts at all times, and interest rates vary so as to ensure that t — 0 at all times. Note that the latter condition ensures that (1.10) and hence (1.11) are also satisfied at all times.)

We turn next to the price-setting decision of sellers that choose a new price at t — 2 to apply beginning in period t. Because such a price is expected to apply in periods t -f j with exactly the same probabilities as for the price pj, the objective of these sellers is simply Et-2$t-i(p), and the first-order condition that determines pi is given by Et-2$t-i(Pt) = 0* Comparison with (1.13) implies that, in our log-linear approximation,
This is our aggregate supply (AS) equation, relating inflation variation to deviations of output from potential. Because prices are set in advance, expectations of future increases in output relative to Ys also raise prices. In addition, inflation declines when the long term real interest rate at t is higher than had been expected at t — 1. The reason for this is that such upwards revisions raise the returns households can expect to earn from their revenues at t. As a result, they are inclined to raise these revenues by cutting their prices. Only surprise variations in the long rate contribute to this term, because only those variations result in changes in the current marginal utility of income that are not reflected in the current level of aggregate consumption demand, and hence in the output gap. Electronic Payday Loans Online