GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.



2.2 The Individuals

We follow an standard overlappping generation model (Diamond [4]). There
are N
t individuals born in period t. Population growths at rate n, thus Nt =
(1 + n)N
t-1, individuals live for two periods and, then, at time t there are Nt
individuals in the first period of their lives and Nt-1 individuals in the second
period of their lives.

When young, each individual supplies inellastically one unit of labor and
divides his income, I
1,t, between consumption and saving. When old, the indi-
vidual consumes the saving and any interest he or she earns. In period zero a
generation of old people provides, as saving, the quantity of K
0 units of capital.
We denote the consumption in period t of young and old individuals as C
1,t and
C
2,t respectively, thus, the utility of an individual born in period t, Ut depends
on C
1,t and C2,t+1. The saving in period t of a young individual is denoted by
S
1,t. The program of an individual born in period t is the following:

Program Ct: Given wt and Rt+1, choose C1,t, S1,t and C2,t+1 in order to
maximize:

Ut(C1,t, C2,t+1) = log C1,t + 1 + ρ log C2,t+1;

subject to:

C1,t + S1,t = I1,t;

C2,t+1 = (1 + Rt+1)S1,t.

The solution to program Program Ct gives the optimal demand function of
good in period t and period t + 1 and the optimal supply of saving. With a
logarithmic utility function the optimal saving does not depen on R
t+1 and the
saving function,
S>1t(It), is:

S1,∙(1) = 2I+tρ = c1ι,t ;

(3)


where c = y+p is the saving’s propensity.

We assume that an individual born in period t, who supplies one unit of
labor, can be either employed or unemployed. If employed, his income I
t is
equal to the net real wage after taxes (1
- τt)wt, where τt is the tax rate on
an employed worker in period t. If unemployed, his income is equal to the
unemployment benefit in period t s
t . The saving of an employed in period t,
S'1. t((1
τt)wt), and the saving of an unemployed, S>U t(st), are given by:

~ _ , , . . , . ~ _ , .
sw,t((1 - τt)wt) = c(1 - τt)wt ; ^Su,t(st) = cst.                (4)

Old people are not taxed, thus the consumption of an old who was employed
in period t is (1 + R
t+1)c(1 τt)wt and the consumption of an old unemployed
in period t is (1 + R
t+1)cst.



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