and.
mæe(ɑo(ʌɪog(l + fco) — v) — A⅛} (8)
We thus obtain the following hybrid solution for the equilibrium investment levels in
human capital under a partnership (here E\ — ownership):
Lemma 8 The equilibrium investment levels under the Eɪ-partnership are:
kf1 = ɑɪʌʃ' — lf for the owner employee Eγ. and
kSx — ɑɔʌ - 1> f°r ^le non-owner employee Eo-
Remark 1 Note that the incentives for the non-owner employee are the same as under
outside ownership and that the partner-employee has socially optimal incentives to invest
when f, > 1 (a similar result as that in the no competition case).
Remark 2 Here, the two employees are perfect substitutes ex-ante. If the two employees
were perfect complements, then a partnership is the same as an employee-coop.
Comparing Ownership Allocations
Comparing the equilibrium investment levels under different ownership structures, using
the previous results summarized in the Lemma above, we obtain the following ranking of
ownership structures under pure internal competition between employees.
Proposition 2 ; When there is competition between employees inside the firm and outside
options bind, then:
1. the customer-coop achieves the first best:
2. When f'>lall other ownership structures give rise to underinvestment:
3. When f'<lall other ownership structures give rise to overinvestment;
4. If jɑi — ⅜∣ =O (employees are ex-ante homogeneous) the ownership structures
ranked in the extent of human capital investment are as follows: employee coop
is the second-best ownership allocation: it dominates the partnership . which in turn
dominates outside ownership:
5. If 'ɑi — ⅜∣ 0 (employees are ex-ante heterogeneous), then the partnership is the
second-best ownership allocation: it dominates the employee coop, which in turn
dominates outside ownership