The name is absent

Heterogeneous Employees and Excess Supply of Ordinary Employees (scratch)

Now we introduce heterogeneity of laborers and more labor market competition into
our model. We assume that the economy has two firms and need total 4 employees: all
the employees’ ex-post capabilities are different (but they are the same ex-ante): two
are good, two are bad. and two are in the middle: and the two bad ones are of no use.
Moreover, again we assume that there is no product competition (e.g. all products have
demand).

We denote the rwo firms by mɪ and mɔ: the three employees in each firm by Ец , £12, E13
and K21,£32,-^23: and the two customers in each firm by Cn,C12 and C21,C⅛2∙ Each
firm can serve only two customers, so that there is no competition between firms in the
product market. Customers are identical and firm have identical assets. That is. for any
of the four employees we have V₁(k_i) — V⅛(⅛_i). To simplify the model, we assume that
ownership is determined ex-ante and there is no trade of ownership titles ex-post.

Emplovee E-_lj has a o_υ probability of being a good employee and ^α⅛ = ɪ- Ex-post,
among all employees there are two good ones with values of vɪ and v² (i.e. v⁰ = v¹_r υ²;
and uɪ > v²) respectively each with the same probability' of ⅛∙: moreover, there are four
ordinary ones with values of υ³ = v⁴ = υ^m > υ⁵ = υ⁶ = υ^b respectively with the same
probability of —ɪ : and denote them as middles ones (v^m) and bad ones (v^b). Formally,
by investing in human capital employee E_τj gets an ex-post value of

with probability 1 — ɑŋ
with probability ɑŋ. ’

where A⁹ > 1 and g = 1.2: and λ^t < 1. and t = m,b: moreover. A^m > λ⁶. Ex-ante
it is not known how each employee Е_г] is ranked. Here, we assume that the value
of the firm’s product is the highest as long as there is a good employee and a middle
employee, i.e.. V (fc⁹, k^m. k^b) = V (k⁹₁ fc⁹, k^m) = V (W. k^m. k^m) = V (υ_g (W), υ_m (k^m)) =
V > V³ + V^m. where. V = f (v, (fc*). υ_m (fc^m)) and f",_ti,. (fc«, k^m) ≡ ^β⅛⅞f"' = O.⁹
Moreover. V (k∖k^m,k^b) ≡V^x > V (k².k^m.fc⁶) ≡ V². that implies that there will be a
competition for E¹.

From the above set up. it is obvious that at equilibrium, each of the two firms in the
economy will have one good, one middle, and one bad employee.

⁹The technical assumption (fe*. A:"¹) = 0 is macle to keep the model simple. It is not critical
for our results.

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