Lemma 5 The First-best choice of investment levels is:
fc∙ = aiλf, - 1.
Note that we must have ff>~χ and a = min(ɑi, c⅛2}. here to guarantee that the first
best investment is non-negative. Again, this requires λ to be large enough.
Employee Cooperative
When the firm is owned jointly by employees, decisions on the use of the firm's assets
must be agreed on by both employees6. The point is that with only two employees
majority voting does not make much sense. This is why we assume that under an emploj∏ee
cooperative unanimous agreement must be obtained7. The main effect of this decision rule,
as we shall see. is to dull competition among employees relative to a customer cooperative.
As before, we consider a two stage bargaining game: If there is no agreement on the use
of the school’s assets then bargaining proceeds to a second stage where employees compete
to provide their services without the school's asset. In this stage the equilibrium payoffs
are such that the customer gets υ and the better employee gets û — υ. Again, these payoffs
are the outside options available to the customer and the better employee in the first
round of bargaining. Just as under outside ownership, the owner(s) of the asset can thus
get at most V — υ in the first round of bargaining. Since the asset is jointly owned by both
employees the?* will negotiate to split this payoff in half. Therefore, the bad employee gets
⅜ (V - υ). and the good employee gets ⅜ (V - û) ÷ (υ - и) = 5 (V + û) - ɪ/. Thus, the
bargaining solution under employee cooperative (when Ei has the higher ex-post value)
is given by:
Lemma 6 The bargaining solution under employee cooperative is:
Agent: employee Ei employee Ei outside owner O customer C
share: ⅜ (V' + υ) — ɪ/ ⅜(V — υ) 0 v
Each employee Ei has an Qτ chance of being a good employee. If the employee is bad
ex post he will simply get a share of the surplus as a co-owner, but his human capital
investment has no value. Therefore, each employee s ex-ante program is:
i (/(λlog(l ÷ ⅛i)) + λlog(l + ki)) -V -ki
(6)
max < α⅛
fci≥0 (
6An alternative formulation which yields the same results is that one employee :s pieked at random to
decide on the use of the 5.rm's asset.
7If we extend our model to three or more employees, then decisions could be taken by majority voting.
Our results would not be changed qualitatively in this extension.
14
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