have an excess supply of agregate savings, which means that young individuals
must save less and consume more. Thus, in order to be rigurous, we should
specify how to raction saving in this situation. Nevertheless, we omit this point
because, as we will see in the next section, this situation never holds.
3 The Collective Agents
3.1 The Union
In each period t there is one union that sets the wage taking into account
that it will affect the effective quantity of labor employed in the way described
by proposition 2.3.1. We assume that the union cares about employment and
compares the wage in period t with the wage obtained in period t-1 and with the
unemployment benefit obtained in period t. These assumptions are formalized
by the following program:
Program Ut: Given wt-1, τt-1 , st-1 , Lte-1, Nt-1, τt and st choose, wt in
order to maximize:
St = ((1 - τt)wt - γt(1 - τt-1)wt-1 - (1 - γt)st)Lte.
Note from the ob jective function of the union, St , that the higher the wage
after taxes in period t, the higher the welfare of the union. The parameter γt
weights the way in which the wage after taxes of the previous period and the
unemployment benefit are compared with the wage after taxes of the period.
We assume that 0 ≤ γt ≤ 1. If γt = 1 the union compares the wage after
taxes of the period only with the wage after taxes of the previous period. If
γt = 0 the union compares the wage after taxes of the period only with the
unemployment benefit. When γt increases the unemployment benefit weights
less in the comparison. The effective quantity of labor employed appears as a
factor in St meaning that if employment increases, the welfare of the union also
increases.
The motivation for this apparently ad hoc utility function is the following:
In the two extreme cases the union compares the wage after taxes of the period
either with the wage after taxes of the previous period or with the unemployment
benefit of the period. The assumption that 0 ≤ γt ≤ 1 is because we think that
both parameters play an important role in the wage setting process. In other
words, we think the when unions (workers) set wages they take into account
past wages and the current unemployment benefit. We use the simplest utility
funtion that reflects this comparison where γt gives the weight given to past
wages and the unemployment benefit. Note also that when γt = 1 the union
maximizes the increase in wages after taxes of all employed workers and when
γt = 0 the union maximizes the wedge times employment. The solution obtained
in this last case is the same than the solution obtained if the union maximizes