20
PEDRO PABLO ALVAREZ LOIS
than the corresponding increase in production when comparing the two equilib-
rium allocations and prices. This intuition is proved more formally in the following
result,
Proposition 4. The short-run response of the price level to an unanticipated mon-
etary policy shock depends positively on the capacity utilization rate at the time of
the shock.
Proof. Combining the cash-in-advance constraint in equation (2.31), evaluated at
equality, and the loan market-clearing condition, WtLt = Dt + Xt, one obtains
PtCt = Mt + Xt
Making use of the goods market-clearing condition, consumption can be substituted
out, which yields
Pt (yt - Kt+1 + (1- δ)Kt - Φ) = Mt + Xt
assuming that capital is kept constant, since the focus is on the intra-temporal re-
sponse of the variables and noting that xt ≡ Xt∕Mt, the previous equation becomes
(3.26) Ptyt = 1 + xt
Taking logarithms in the previous equation and differentiating it with respect to
the gross rate of monetary growth, it follows that
/o 27a ^ɪɑg (P⅛) ^ɪɑg (M) = 1
’ dlog(l + a⅞) dlog(l + a⅞)
Now, from the previous results the response of output was shown to be positive
and negatively related to the capacity utilization rate of the economy. Hence, the
response of prices is larger the smaller is the effect on output. □
Up until now, the short-run or impact effects of a monetary shock have been
explored. However, in order to explore the dynamics of the model, it is necessary
to determine the equilibrium laws of motion of the theoretical economy by means
of a numerical approximation algorithm. This is precisely the objective of the next
section, where the quantitative properties of the model are evaluated and simulation
exercises are performed as well.
4. Quantitative Analysis
In this section, I describe the quantitative properties of the model economy. The
objective is to illustrate the interactions between capacity utilization and mark-up
rate changes by analyzing numerically the dynamic behavior of some key macroe-
conomic variables in response to a monetary shock. One of the results I pursue is to
show how the same shock can have significantly different short run effects depend-
ing on the characteristics of the economy at the time the shock occurs. The variable
of reference is the level of the capacity utilization rate. In order to compute the
impulse response functions, the model has to be solved numerically. The solution
method adopted is based on a linear approximation of the equilibrium policy rules
about the non-stochastic steady state.