Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

incentive for stimulating the economy at zero inflation, as described in Kydland and
Prescott [1977] and Barro and Gordon [1983].

4.2.2 An inflation bias equilibrium

Figure 4 displays the consistent steady-state equilibrium, in which agents correctly fore-
cast the incentives of the monetary authority. Panel A shows the policymaker’s objective
function, which can be thought of as an indirect utility function: the relevant portion
for the current discussion is the solid line, which reaches a maximum at the value of
m/m* =1.01. This implies a stationary relative price (po) of 1.022, which is determined
along the lines of Figure 2 with agents expecting p⁰₀ = p0 and m⁰ = m. Given that there
is a steady state, π = po and this relative price thus implies an inflation rate of 2.2 %
per quarter. At this inflation rate, the monetary authority faces sufficiently increasing
marginal relative price distortions that it chooses not to further increase m in an effort to
further reduce the markup. Notably, the stationary markup departs little from its value
at zero inflation. Stationary consumption is 99.96% of its zero inflation value, so that
the markup has changed negligibly (recall that the markup and consumption are directly
related by μ_t = (c_tχ)^-1 with the preference specification used here).

4.3 Pessimistic Equilibrium

We next suppose that the monetary authority instead knows that the high po equilibrium
will always prevail. Its incentives are sharply different. Looking at Figure 4, we can see
these incentives in the dashed lines, which describe a non -equilibrium situation in which
the private sector and the monetary authority assume that the future is described by
m,Pθ while the present is described by po. The monetary authority has a clear incentive
to raise m > m since this lowers the markup and relative price distortions, with utility
being maximized when m is sufficiently high that there is exactly a tangency equilibrium
in the temporary equilibrium analysis of Figure 2. Here the monetary authority “takes
policy to the limit” of the set of equilibria that are imposed as its constraints. Because
Figure 4 assumes optimism (that is, the low-po outcome occurs with probability one) ,
there are some inconsistencies in using Figure 4 to discuss an equilibrium with pessimistic
expectations. Notably, the monetary authority can lower the markup to less than one, in
which case some of the firms in the economy are making losses. But the picture tells the
right story: nearer the consistent discretionary equilibrium that is described by a level

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