the steady states from Figure 1. The solid line is the best-response function when agents
expect p0 in the future, with certainty. The low steady state is a point-in-time equilibrium
when agents expect po in the future, but the high steady state is not, because in that
steady state agents expect po rather than po in the future. In fact, the second point-
in-time equilibrium must be at a higher p0 , because expectations make the future less
important than in the steady-state analysis of Figure 1: a larger increase in the weight
on the future is required for the second fixed point to occur. The dotted line shows the
best-response function when agents expect po in the future, with certainty. In this case
the higher of the two steady-state equilibria survives as a point-in-time equilibrium, but
the the low-inflation point-in-time equilibrium is now higher than the low-inflation steady
state.
From (23), note that for given m0, lower m drives down the lower price equilibrium
and drives up the higher price equilibrium. Lower current m shifts the best-response
function down, with lower current marginal cost reducing the firm’s optimal price for any
price set by other firms. The lower fixed point falls, but because the basic properties of
the response function are unchanged, there is still a second fixed point, now at a higher
level of po ; at this high level of po , high future marginal cost offsets the lower current
marginal cost. Current monetary policy actions thus affect the two equilibria in very
different ways.
Figure 2 illustrates that beliefs about both current and future equilibrium selection
can affect the opportunities available to a discretionary monetary authority. Raising the
current money supply shifts out the best-response function for firms, resulting in a lower
high-po equilibrium and higher low-po equilibrium. The likelihood of each equilibrium in
the present will thus alter the trade-off facing the monetary authority. Beliefs about future
equilibrium selection shift the current period best-response function for a given current
money supply, and thus also alter the trade-off facing the current monetary authority.
4 Discretion under perfect foresight
In a perfect foresight discretionary equilibrium, the current monetary authority sets the
money stock to maximize the representative private agent’s welfare, subject to
1. The behavior of the future monetary authority (m0).
2. The behavior of firms in the future (p0o).
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