Ch. 8: Conglomerate Firms and Internal Capital Markets 445
Fig. 2. Optimal production with differing ability across industries.subscripts and definingvi=dipi−ri, it can be shown that the optimum output for a
firm, assuming conglomerate production, is given by
k 1 =
(α+β)(d 1 p 1 −r 1 )−β(d 2 p 2 −r 2 )
2 α(α+ 2 β)=
(α+β)v 1 −βv 2
2 α(α+ 2 β),
k 2 =(α+β)(d 2 p 2 −r 2 )−β(d 1 p 1 −r 1 )
2 α(α+ 2 β)=
(α+β)v 2 −βv 1
2 α(α+ 2 β),
forv 2 >βv 1 /(α+β)andv 2 <(α+β)v 1 /β. For values ofv 1 ,v 2 outside of this range,
a firm will choose to be a single-segment firm.
Figure 2illustrates which firms choose to be either conglomerates or single-segment
firms. Lettingθ =(α+β)/β, we can illustrate optimal organizational form across
industries.^21 Ifv 2 >θv 1 , then the firm will produce only in industry 1, so that
k 2 (v 1 ,v 2 )= 2 (αv+^2 β)andk 1 (v 1 ,v 2 )=0. Similarly, ifv 1 >θv 2 , thenk 1 (v 1 ,v 2 )=
v 1
2 (α+β)andk^2 (v^1 ,v^2 )=0.
Firms in region II optimally choose to be conglomerates, whereas firms in regions I
and III choose to produce in a single segment. Specialization is optimal if the firm is
much more productive in one industry than the other; diversification is optimal if the
productivities are similar. Thus, the decision to diversify depends in part on the firm’s
comparative productivity in the two industries. An implication of this result is that,
all else being equal, a conglomerate’s large segment is more productive than its small
segment.
The relation between productivity and focus in a population of firms depends both
on the distribution of ability within these firms and on the distribution of ability across
firms. If organizational talent is industry-specific, firms that are highly productive in
(^21) The figure assumes thatr 1 =r 2. More general cases are discussed inMaksimovic and Phillips (2002).