Our results have far reaching implications for several of the applications of our model
that we have in mind. As will become clear this general result can be extended under
certain conditions to situations where emplovees compete both in internal and external
labor markets.
INTERNAL AND EXTERNAL LABOR MARKETS
In the previous section we considered only competition between employees within a
single firm. This is the only possible form of competition if employees'* investments in
human capital are entirely firm-specific, or if employees are entirely locked-in their firm
for other reasons. In practice there is always some form of lock-in of employees. However,
despite the likely presence of some lock-in it is not always appropriate to assume that
lock-in is total. Indeed, in some labour markets competition between employees across
firms can be more important than competition within a single firm. Therefore, we extend
the model in this section to allow for both competition within and between firms. As a
first step we shall consider the polar case where there is no lock-in of employees at all and
compare our results to the previous polar case with total lock-in.
We consider the simplest possible extension with only two firms and two employees in
each firm. We shall make the obvious adaptations from the previous setting to introduce
competition for employees between firms.
We denote the two firms by mɪ and mɔ: the two employees in each firm by E*ι1, £*12 and
^2i,-E⅛ æɪd the two customers by C1 and C2. Each firm can sene only one customer,
so that there is no competition between firms in the product market. Customers are
identical and firms have identical assets. That is. for anj, of the four employees we have
½(⅛v)=½(⅛)∙
As before, all employees are identical ex ante. In period 1 they invest in human capital
and the values of their investments are again random. We consider a similar stochastic
structure as before, where ex post one employee is more valuable than the others and
each employee is equally likely ex ante to become the better employee ex post (at equal
investment levels): each employee now has a ɪ probability of being a good employee.
That is. by investing ⅛ in human capital employee i gets an ex-post value of v(⅛) =
Îu, with probability $
Alog(l + ki), with probability ɪ.
Again, we assume that Vf(k1.k∙2) = max{V'1(kι). V3(⅛2)}. That is. the best employee
determines the value of the firm’s product. Since there is only one good employee ex
20