The name is absent



and,

m⅞⅛ (/'Λ1 log(l + ⅛n) + λ2 log(l + fcn)) + Ц^Л"’ ɪog(l ÷ ⅛n) - fcn} (16)

VVe thus obtain the following solution for the equilibrium investment levels in human
capital under a partnership (here
Ep-ownership):

Lemma 13 The equilibrium investment levels under the Ep-partnership are:

k?* °tp%1 + A2) ÷ ——ɑp) ʃ ʌm _ ɪ. yor partner Epι and
k∑* ≈ ~
(/'A1 ÷ A2) ÷ q--Aγπ — 1, for the non-owner employee En.

That is. the partner invest at first best level: while the non-partner employee will under-
invest if ∕' > 1.

Employee Coop

• Bertrand competition between employees results in equilibrium payoffs in the second
stage of the bargaining game where employee
E1 gets vɪ — ιr, each customer Cij
gets u5t other employees Es get vλ — vj+1 and the worst two employees Et get 0.

• In the first stage of the game, when f' > 1. Bertrand competition for the good
employee results in a wage for employee F1 of V1τ72. and a wage of 0 for the other
employees. Each customer gets
vb and all the employee-owners divide the residual
equally i.e. each gets ∣(V2 -ub). Note that this equal sharing rule will lower the
marginal incentives of an employee being a middle one ex post, without improving
any other cases. Thus it is the source of an inefficiency.

Thus, when ∕' > 1 the bargaining solution under employee cooperative is given by11:

Agent:      employee E1 employee E3 customer Ci

share: V1 — V2 + ∣(V'2 ~ vb) ∣(V2υb) υb

where 5 = 2, m, b,

These payoffs then translate into the following ex-ante investment choices for the em-
ployees. VVhen ∕' ≥ 1 they choose their investment in human capital
ki to maximize:

1 ɪ Here we assume also that ɪ(V2 - υs) > v2 - v3 .

When ∕' < 1 . so that. V1V2 < vl - v2. and (V^2 - v5) > t∙2 - v3. the bargaining solution is:
Agent:      employee Z1 employee
Es employee Et customer C1

share: υ1 - v2 τ (V'2 - υs) ɪ(l ɔ - υ5) ɪ ( V2 - v5) v5



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