Technological progress, organizational change and the size of the Human Resources Department

opportunities over the longer term and the difficulty of designing compensation
mechanisms to give managers and employees appropriate incentives to control costs
and product quality¹⁰. Here, we rely on this debate on the “make or buy” decision
by accounting for the fact that firms relying on large human resources departments
are characterized by specific management costs (bureaucratic and incentives costs)
labelled as vertical coordination costs.

We now make clear two working assumptions for the optimization problem of the
firm to make sense. We first need to ensure that function C (n, ρ) is increasing
in n and decreasing in ρ. We need the latter condition on ρ to have an interior
solution to the optimization problem tackled. Indeed, an increase in ρ decreases
production labour, and therefore production. To balance this negative impact on
profits, we need the increase in ρ lowers the coordination costs. With analytical
forms postulated, we need the decrease in horizontal coordination costs due to an
increment in ρ more than compensates the induced rising vertical coordination costs
(when η>0). This property will be put in more formal terms in Proposition 2.

The convexity of the cost function can be easily investigated. We have the
following result:

n∙        n       nξ∙(1-ρ. )^θ∙ρη

Proposition 1 The cost function C(n_t,ρ_t) = ^{t l} J^,t ^tt is convex when ξ > 1,
θ<1 and η is small enough (either positive or negative).

Proof. The first-order partial derivatives of the cost function are given by:

∂C   nt^ξ        θ-1 η-1

∂ρt_t = di,^{(1 - ρ}t)   ^{ρt lη -} (^{η + θ}) ^ρt]
while the second-order partial derivatives are:

^ξ (^{ξ - 1}) ^nξ 2 ^{(1 -} Pt)θ Pt
dt

∂^c- =   '. (1 - Pt)^θ-1 ρη^-1 lη - (η + θ) Pt]

∂nt ∂ρ_t       dt          ^{t t                    t}

nt^{(1 -} ρt)^θ-2 ρ¹i~^- [η (η ^{- 1)(1 -} ρt) ^- ρtη (θ ^{- 1}) +

^-ρ,η (η + θ)(^{1 -} ρt) ^{- ρ}2 (η + θ)(θ ^- 1)]

and the hessian matrix is:

∂²C     ∂²C

∂n2    ∂ρt∂nt

∂²C     ∂²C

∂nt∂ρ_t     ∂ρ2

¹⁰ However, as highlighted by Joskow (2003), this literature has focused much more on the ineffi-
ciencies of market transactions than it has on the strengths and weaknesses of internal organization.
Our focus on vertical and horizontal coordination costs can therefore provide an interesting com-
plementary contribution to this debate.

11

<<   8   9   10   11   12   13   14   >>

More intriguing information