CAPACITY AND ASYMMETRIES IN MONETARY POLICY
17
From (2.3), the capacity utilization rate can be alternatively expressed as
(3.15)
Ci _ (Pt∕Pt)
t Vt
Substituting the price relation for its value given in (2.6), it follows that the capacity
utilization rate depends only on vt, the cut-off value of the idiosyncratic shock
(3.16)
1 I f'vt
Ct ≡ C (vt) = -U
Vt Jv
υ't
Vt
Since, in the short-run, the capacity utilization rate increases after a positive mon-
etary policy shock, the cut-off value vt must decrease (recall that the price relation
(Ft∕Pt), is a decreasing function of ¾).
Notice that the weighted proportion of firms with idle resources, π (¾), depends
positively on vt, as becomes clear after rewriting (2.18) as
r l∙τ, , . -, -1
(3.17)
τr (¾)
Thus, the unanticipated monetary policy shock increases the mark-up since this
variable, defined as,
(3.18)
Z i V1
Mark-Up =(1---,—г I
∖ eπ(vt)J
depends negatively on the proportion π (¾).
It is worthwhile stressing the highly non-linear relationship that exists between
the mark-up and the capacity utilization rate. This means that in a high capacity
economy, the effect on the mark-up of an extra increase in the capacity utilization
rate due, for instance, to a monetary policy shock will be higher than the effect
of the same policy in a low capacity economy. Next, I analyze the response of the
nominal interest rate and the real wage rate to an unanticipated monetary policy
shock.
Proposition 2. For a fixed level of investment and the utility function in (2.30a),
the impact effect of an unanticipated monetary policy shock on the nominal interest
rate is negative, while the real wage rate responds positively to the same shock. That
is,
dlog (1 + Rt)
d log xt
and
WP).,≡^Γzp,*>θ
d log xt
Proof. From (2.33) and (3.10), the equilibrium real ware rates is given by
(3.19)
ж
pt
l-7 (I-Lt)
Taking into account the final-goods market clearing condition, this can be expressed
as
(3.20)
Wt
pt
7 yt - Kt+1 + (1- δ)Kt + Φ
1 -7
(1 - Lt)