14
PEDRO PABLO ALVAREZ LOIS
importance of their production in total output. An important feature of this equi-
librium is its symmetry: all input firms j choose the same capacity level and take
the same pricing decisions. With all prices identical, aggregate employment, de-
noted by Lt, is equal to individual expected employment levels (up to a scaling
factor) :
(3.1)
lp7) At , , Kt Γ , .
Lt = --Δ Ya VtdF + Kr dF
AfAj Jv Jvt
where Kt and Xt stand for aggregate capital and capital∕labor respectively at time
t — 1 and available at time t, and
(3.2) ¾ = . ∖ _6
yt
~y ∖pt)
represents the ratio of productive capacity to expected demand for intermediate
inputs. Notice that, as ¾t > O, the aggregate productive capacity is underutilized
at equilibrium. The individual capacity utilization rates are given by:
(3.3)
Cj,t
(g-)^⅛,t∕⅛
1
if
if
which introduced into (2.1) yields the aggregate capacity utilization rate,
(3.4) Ct ≡ ½
ɪt
For a given distribution F (vt) and thus given σ^, there is a decreasing relationship
between the capacity utilization rate, Ct, and the weighted proportion of firms
with idle resources, π (¾), which subsequently determines the mark-up rate. The
aggregate capacity utilization rate is directly linked to the proportion of firms that
produce at full capacity, (1 — π(¾)). At given price elasticity of demand, e, this
implies a positive relationship between the capacity utilization and mark-up rates
Mark-Up ≡ 1 -
-ɪ-
eπ (¾)
-1
3.2. Implications for Short Run Dynamics. Next, it is presented a diagram-
matic representation of the labor market equilibrium at given capacity level that
will prove useful for understanding the short-run implications of the model. Specif-
ically, the diagrammatic apparatus will provide good intuition on the interactions
between capacity utilization and markup variations in the short run. As a result,
it will be very useful to understand why the short run effects of a same shock are
expected to depend crucially on the value of the capacity utilization rate at the
time the particular shock takes place.
In Chart 1, the upward sloping curve represents the aggregate labor supply sched-
ule, as given in equation (2.33). The other curve, concave and sloping downwards,
represents the macroeconomic labor demand curve given in equation (3.1). In the
very short run, at given capacity, the labor demand curve intersects both axes. The
intersection with the horizontal axis is due to the fact that even at zero real wage
rates, the short-run demand for labor is bounded above by the maximum number
of work stations corresponding to the full employment of installed capacities.