476 V. Maksimovic and G. Phillips
whereλss=( 1 −λc)/2. We assume that the capacity in each industry is fixed atKifor
i=1, 2.
The profit function of a single-segment firm that operates only in industryiis, as
before
pikssi −rikss−βi(
kiss) 2
.
Maximizing profits yield an expression for optimal output analogous to that in the single
industry case above, so thatkssi =pi 2 −βri.
A conglomerate’s profit function is given in equation(2)in the text. For the special
case discussed here it can be rewritten as
d 1 cp 1 kc 1 +d 2 cp 2 k 2 c−r 1 kc 1 −r 2 kc 2 −β(
kc 1 +kc 2) 2
.
We want to show that following a positive price shock in industry 2, conglomerate
segments that are less efficient than the competing single segment firms in industry 1 be-
come smaller relative to the single segment firms in industry 1, so that the ratio(kc 1 /k 1 ss)
declines with increases inp 2. We thus assume thatd 1 c<1 and, without loss of general-
ity,d 2 c=1.
By solving forkci andkssi and substituting into the industry equilibrium conditions
σ+ρri=(λckic+λsskiss)nwherei=1, 2, we can solve for the price of capital in
each industryr 1 andr 2. Substitutingr 1 andr 2 back into the expressions forkciandkssi,
we obtain
δ(k 2 c/kss 1 )
δp 1=−A
(
nλss
nλss+ 2 β(v+wj)−dc 1)
.
It can be shown thatAis positive for feasibleλss(λss< 0. 5 ). Thus, for all sufficiently
lowd 1 c(d 1 c<nλssnλ+ss 2 βρ)the result follows. Note that if the supply of capacity is fixed in
each industry so thatρ=0, it is sufficient thatd 1 c<1.
Case (a) can be shown similarly. We can also show that:
Remark 4.The greater the productivity of a conglomerate’s operations in an industry,
the greater the effect of price shocks in that industry on the optimal size of operations
of the conglomerate in other industries.
Thus, we would expect that shocks in a conglomerate’s main segment (which, all
else being equal, has a higher relative productivity) would produce greater effects
on the industries in which it has its peripheral segments than if the opposite were
true.
Note that we do not predict this pattern of growth across conglomerates business
units because the conglomerate firms have an internal capital markets that are superior
to those of single-industry firms. Rather, they result from the comparative advantage
of conglomerates and single-segment firms over different ranges of demand. Moreover,
the predictions of model differ from the agency or empire building models in the liter-
ature. The agency and empire building models predict that if a conglomerate receives