QUEST II. A Multi-Country Business Cycle and Growth Model



U1F10 = *26/ / N1 + v(Flv


Flv )+ E1 ∆F+ι


and


(22a)


ulFf, =-9&, + τ(.)()0 -f;)+ (,∆)+,


(22b)


The return from an occupied position is the pure after tax profit of the firm minus the risk
that a position becomes vacant because a worker quits the job
T, thereby incurring search
costs for the firm. The value of a vacant position is minus vacancy costs plus the prospect of
filling the position. It is assumed that both parties know about the profit opportunities of
their respective opponents. Firms and workers (trade unions) solve the following Nash
bargaining problem by setting wages such as to maximize the product


0D[( +; - + )β ()0 - Flv )(1-β)


(23)


This agreement is based on the relative bargaining position of the two parties. The
bargaining strength of workers is characterised by the parameter β (0
β1) which
determines the fraction of total profits from a successful job match going to workers. The
solution of this bargaining problem yields the following division of the surplus from a job
match



,  β(1 WO)  ` ( + - +“ + Fl0

(1 + (1 - β)VFF ) '



(24)


This equation also shows how marginal tax rates affect the worker's share in total surplus
from a job match. A decrease in the marginal tax rate will increase their share. This reaction
can be understood by noticing that workers and firms are cooperating against a third player,
in this case the government, in order to minimize their tax burden. Since a unit rise in wages
conceded by the firm yields only relatively small net benefits to workers under high
marginal tax rates, it is optimal for firms and workers under a cooperative outcome to have
a smaller share in total surplus. As a full solution of the maximization problem (23), the
following wage equation can be obtained.

(1 - β) /                β I /     < <   sure(.)YFr

(—(% ( BE1, + /EI6, ) + . β 4 <! (α + η(1 - α)) ɪ + -—
(1 - WO Y '        '1 (1 + VFF )P            1 N, τ (.)

(25)


Gross wages are positively indexed to labour productivity with indexation depending on the
bargaining power of workers. More precisely, in the case of perfect competition in the
goods market, wages are linked to the marginal product of labour, while in the case of
imperfect competition and positive β, there exists some rent sharing between workers and
firms. Wages also depend on the reservation wage which is composed of unemployment
benefits and the value of leisure, which as noted above can be expressed as a function of
household wealth and the average hour of work supplied per period. Provided workers have
market power they can ask for real wages which exceed the reservation wage. Real wages
also depend negatively on the unemployment rate, since a high unemployment rate has an
adverse effect on the probability of finding a job. Equation (25) also shows how labour
taxes and social security contributions affect real wages. An increase of either component
would make leisure (unemployment benefits) more attractive relative to work and wage

14



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