As the preceding discussion has made clear, all shocks in this economy are individual shocks.
Nevertheless, the individual shocks that cause matches to break up and shops to enter or leave
particular markets do have aggregate consequences because there is only a finite number of
agents. So, in general, the economy will not settle down to a deterministic steady state unless
we turn off these shocks. If we do turn off all shocks, there is a deterministic equilibrium
that the economy would stay in if left undisturbed by entry and breakups, with wages being
adjusted each week. This equilibrium will serve as an initial position for all the
experiments we perform on the model below.
The equilibrium is one in which all the potential gains from trade are realized. Each
person is matched with one employer and two stores. There are n shops, one trading in
each of the n goods. To preserve symmetry across goods, we suppose that each good is
the primary consumption good for exactly one shop owner. Each shop begins every week
with actual and target input both equal to n which is the number of suppliers of each
good, and with actual and target sales equal to inventory holdings equal to actual output.
Thus, the economy's total output equals full capacity, y = n (n - 2 - F).
In AGH (2011), we characterize the rest of this equilibrium, which will repeat itself
indefinitely, with all nominal magnitudes { money and bond holdings, actual and effective
wages and prices, and permanent incomes { rising each week at the constant target rate of
in
ation, provided that the fixed cost of operation F is small enough that shops always pass
the profitability test during the exit stage.
In
ation has almost no effect in this
exible-price equilibrium without any shocks. There
will be a minor effect on the equilibrium tax rate because, with higher in
ation, the
government is collecting more seigniorage and, hence, can maintain its target real debt level
with a lower sales tax. However, aggregate output and employment will be unaffected, the
real rate of interest will remain equal to the rate of time preference, and the volatility of
output and in
ation will remain equal to zero.
When the shocks are turned on, the economy ceases to track full employment and full
capacity. In particular, GDP falls whenever a shop that was satisfying some consumers goes
out of business or a customer loses a store because of a random breakup. GDP also falls