stock of human capital, in order to fund valued public education. Thus, the future tax
rate effectively responds to expectations of the future tax rate. Or, equivalently, an indi-
vidual agent’s current decision about human capital accumulation depends on aggregate
decisions because the aggregate determines the future state (capital) to which policy will
respond. For certain parameterizations the policy response induces sufficiently comple-
mentarity among private agents’ decisions that there are multiple equilibria. Again, with
commitment the multiplicity disappears.
8 Summary and conclusions
We have described equilibria under discretionary monetary policy in a basic New-Keynesian
model with two-period staggered price setting. The trade-off that our monetary authority
faces is a familiar one. Output is inefficiently low because firms have monopoly power.
This creates an incentive for the monetary authority to provide unexpected stimulus, ex-
ploiting the pre-set prices and raising output. However, when it exploits pre-set prices,
the monetary authority also raises the dispersion of prices, leading to an inefficient al-
location of resources. In equilibrium, the monetary authority is balancing the marginal
contribution of these two effects.
While the monetary policy trade-off is familiar, the nature of equilibrium is not. Dis-
cretionary monetary policy leads to multiple equilibria. The multiplicity occurs because
of complementarity in pricing behavior that is induced by the monetary authority’s nat-
ural tendency to treat the level of pre-set nominal prices as a bygone. Under discretion,
in each period the monetary authority moves the nominal money supply proportionately
with the nominal level of pre-set prices. This feature of monetary policy means that
higher prices set by firms in the current period will lead to a higher money supply (and
even higher prices) in the subsequent period. Understanding this mechanism, an indi-
vidual firm adjusting its price in the current period finds it optimal to raise its price in
response to higher prices set by other firms. There is complementarity in pricing, and it
leads to multiple equilibria.
When we consider discretionary equilibria that are driven by a sunspot variable, the
equilibria involve random fluctuations between different real outcomes.14 If all firms
14 The distribution of the sunspot variable shifts the equilibrium, and while we do not pin down that
distribution, it is an integral part of the definition of equilibrium. Thus far, we have only considered i.i.d.
sunspot variations, so as to produce the simplest possible explanation of the source and nature of multiple
equilibria. In future work, we plan to extend the analysis to the implications of persistent sunspots. This
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