5 — c. Accordingly, in a zero inflation stationary state, utility is just ln(1) + 0.9 ∙ (5 — 1).
A first-best outcome would dictate that u(c, l) be maximized sub ject to c =(1- l). For
the specified preferences, this leads to a first order condition П = χ or an efficient level of
work (n) of 1.11. So, the increase in work from cutting the gross markup to one is 11.1%.
4.2 Optimistic Equilibrium
If the discretionary monetary authority knows that the low equilibrium will prevail, then
its problem is to maximize
u(c, l) + v(po0; m0)
where v(po'; m') denotes the future utility that corresponds to a steady state with m0 and
selection of the low-p0 equilibrium with probability 1.0. The maximization is subject to
c = c(m,po)
l = l(m,po)
P0 = r(p0,p00,m, m0),
where r () denotes the response function on the right hand side of (23), and the presence of
po instead of po is meant to imply that we place probability one on the low-po fixed point
of the response function. The monetary authority understands that future utility and
current price determination is influenced by the actions of the future monetary authority,
but has no way of influencing its behavior or the future price that will prevail. So, the
monetary authority maximizes current period utility.
4.2.1 Exploiting initial conditions
Figure 3 provides some insight into the nature of the monetary authority’s choice when
it knows that the po equilibrium will prevail for all time. For this figure, we assume
that future monetary policy is noninflationary (m0 = m*, p0 = 1). The current monetary
authority optimally adopts an inflationary monetary policy (choosing m > m* = 1)
because it can reduce the markup and stimulate consumption toward the first-best level.
It does not completely drive the gross markup to one because an increase in m produces
relative price distortions. While the relative price distortions are negligible near the
noninflationary steady state, they increase convexly as monetary policy stimulates the
economy. Figure 3 illustrates the sense in which New Keynesian models capture the
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