Qualification-Mismatch and Long-Term Unemployment in a Growth-Matching Model

not accumulate any additional knowledge, i.e. without allocating any resources to
the long-term unemployed, they are not able to handle the latest production tech-
nologies. Therefore, the number of long-term jobless workers depends positively on
the unemployment duration p and positively on the rate of technical progress λ.

If new job-matches are formed, each match generates additional revenues and,
because both trading partners have monopoly power,¹⁰ unemployed workers and
firms could bargain over the additional produced profits; or the profits are simply
shared using a sharing rule. This sharing rule determines the profit proportion,
the new workers get and therefore, the wage results as a constant fraction of the
marginal product

w = xF∣(k), 0 < ω < 1,                          (6)

with ω denoting the sharing proportion and it represents the monopoly power of
unemployed workers.

The Goods Market

Each firm uses capital K, labor L and the current state of technological progress
X := ʌoeʌ^t to produce a homogenous good X. Production is described by a Cobb-
DouglasTunction:

X = F (K, XE ) := K [XE ]¹^^α                (7a)

^ x = k^a                                    (7b)

with x := X∕XE and k := K∕XE.

For the representative firm demand decisions concern changes in real capital and
in employment. It is supposed that installation costs of a I [with 0 < eʃ < 1] arise
with c/ as the fraction of installation costs used for investments I.

The change in employment is determined by inflows in and outflows out of unem-
ployment. The inflows into unemployment are characterized by the separation of
existing job-matches at any point in time and are described by the exogenously
given separation rate v times the workers E. Thus, inflows characterize the num-
ber of unproductive jobs which generate layoffs.¹¹ On the other hand, outflows

¹⁰See also Nickell (1999) and Zaxchi (2000) for a recent discussion of the wage determination
in search models.

¹¹For an exogenous separation rate see also PlSSARlDES (1990) and PθSTEL-VlXAY (1998) and
for an endogenous rate see Mortexsex∕Pissarides (1994, 1998).

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