Horizontal coordination costs are the firm-level costs of coordinating the tasks real-
ized by each production worker. They embed switch costs between tasks, inter-tasks
learning and information sharing costs, but also the strain associated with versatility
and stressful working conditions. The higher the number of tasks per worker, the
higher the switch costs, the higher the inter-tasks learning and information sharing
costs and the higher the stress costs. Since production workers are in fraction 1 - ρ,
we assume that the costs of coordinating n tasks for each worker writes:
h (n, ρ) = nξ • (1 — ρ)θ
where ξ, θ > 0 (we do not impose ξ 6= θ).
In other words, the costs of horizontal tasks coordination are based upon the idea
that allocating workers’ attention over various activities is likely to raise the oc-
currence of mistakes on the job. This increasing risk of production failure reduces
the value of output and profits by an amount that depends both on the number of
tasks per capita n and on the size of the production service (1 — ρ), given elasticities
parameters ξ and θ that will be discussed below.
Vertical coordination costs are the costs of coordinating workers. Consistently with
Section 2, they reflect the administrative cost of running a human resources depart-
ment in a firm. In our set-up, such a cost involves of course a direct labour cost,
which is already accounted for by the last term of the profit expression given above,
but also an extra-cost depending on the size of the human resources department to
be operated. To this end, we assume that vertical coordination costs is a function
of the share of workers in the human resources service, that is:
v (ρ) = ρη
where η can be positive or negative. In particular, when η>0 (that will be the case
considered in the simulations) vertical coordination costs increase with the increase
in the share of workers in the human resources service (and this corresponds to a
more bureaucratic situation). On the other hand, when η<0 coordination costs
decrease with the increase in the proportion of human resources employees in the
economy (and this can be interpreted as a less bureaucratic scenario).
The fact that vertical coordination costs are linked to the size of human resources
service and add to the wage bill can be related to the literature on vertical inte-
gration. Indeed, since Williamson’s theory of transaction costs, it is well known
that a major limit to the growth of firms lies in the costs of internal organization.
As explained by Joskow (2003), the volume of auditing information that must be
processed by management grows non-linearly with the size and scope of the firm and
becomes more difficult to use to control costs and quality effectively and to adapt
to changing market conditions. Moreover, monitoring becomes also more difficult
in large organizations and there are therefore potential shirking problems resulting
from low power internal compensation incentives. In sum, the decision whether or
not to vertically integrate comes from a tradeoff between the costs of market-based
arrangements and the costs of internal organization described by the relatively in-
ferior adaptive properties of bureaucratic hierarchies to rapidly changing outside
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