The name is absent

dlog (Π^z_t∕P_t) ₌ 7  /dlog (¾) _ dlog (I-L_t)

d log x_t       1 - 7 ∖ d log x_t       d log x_t

which is positive since in the previous proposition it was proven that employment
and output are positively related to an unanticipated monetary policy shock.

Now, from (2.16) one can solve the gross nominal interest rate as a function of
the mark-up, the ratio of intermediate to final-good prices and the wage rate as
follows,

Consequently, the effect on the nominal interest rate due to the unanticipated
monetary shock acts through three channels, namely the mark-up, the price relation
and the real wage rate:

dlog(l + ¾) _ dlog (1 — l∕eτr (⅞)) dlog(F_t∕P_t) dlog(TV_t∕P_t)

(3-23) ---—:-------- — ------—:--1--—:--ʌtʌt ---Tj--------

d log x_t             d log x_t            d log x_t               d log x_t

The monetary shock rises employment and final output implying a reduction in
the real wage rate. As discussed above, higher employment levels imply a higher
capacity utilization rate and other related variables such as the mark-up and the
proportion of firms producing at full capacity, 1 - π (¾), so that,

∕dlog (1 — l∕eττ (¾))

sign ------71-----------

∖ d log x_t

Moreover, the price ratio decreases in response to an unanticipated monetary shock.
This is so because from (2.6) this ratio depends only on the cut-off value ¾, which
is negatively related with the equilibrium level of employment

From the discussion above, it follows that the derivative in (3.23) is negative. □

Altogether, this version of the model displays the liquidity effect of a money
supply shock, as well as the other features that characterize monetary economies.
As noted above, the presence of capacity constraints as well as the monopolistic
competitive environment provide a rich source of dynamics. This point will be
discussed in more detail below.

Proposition 3. The magnitude of the response of employment (output) and the
real wage rate to an unanticipated change in the growth rate of money is nega-
tively related with the capacity utilization rate at the time of the shock, whereas the
opposite is true for the nominal rate of interest.

Proof. The strategy of the proof is the following: first it is shown that the magnitude
of the response of employment to the monetary shock depends negatively on the
level of employment at the time of the shock; next it is proven that in a high (low)
capacity economy employment will be higher (lower).

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