The name is absent

and,

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

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

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

k?* °^tp% (λ¹ + A²) ÷ ——ɑp) ʃ ʌm _ ɪ. y_or partner E_pι and
k∑* ≈ ~ (/'A¹ ÷ A²) ÷ (ɪ ^q--A^γπ — 1, for the non-owner employee E_n.
∙

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 u⁵_t other employees E^s get v^λ — v^j+1 and the worst two employees E^t 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 V¹ — ^τ7². and a wage of 0 for the other
employees. Each customer gets v^b and all the employee-owners divide the residual
equally i.e. each gets ∣(V² -u^b). 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 ~ v^b) ∣(V² — υ^b) υ^b

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 k_i to maximize:

¹ ɪ Here we assume also that ɪ(V² - υ^s) > v² - v³ .

When ∕' < 1 . so that. V¹ — V² < v^l - v². and ∣(V^² - v⁵) > t∙² - v³. the bargaining solution is:
Agent:      employee Z¹ employee E^s employee E^t customer C₁

share: υ¹ - v² τ ∣(V'² - υ^s) ɪ(l ɔ - υ⁵) ɪ ( V² - v⁵) v⁵

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