GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

2.2 The Individuals

We follow an standard overlappping generation model (Diamond [4]). There
are Nt 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 N_t
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, I1,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 K0 units of capital.
We denote the consumption in period t of young and old individuals as C1,t and
C2,t respectively, thus, the utility of an individual born in period t, Ut depends
on C1,t and C2,t+1. The saving in period t of a young individual is denoted by
S1,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 Rt+1 and the
saving function, S>1t(I_t), is:

S1,∙(¹∙) = 2I+^tρ = c¹ι^,t ;

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 It 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 st . The saving of an employed in period t,
S'1. _t((1 — τ_t)w_t), and the saving of an unemployed, S>U _t(s_t), are given by:

~ _ , , . . , . ~ _ , .
^sw,t^{((1 - τ}t)wt) = ^c(^{1 - τ}t)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 + Rt+1)c(1 — τt)wt and the consumption of an old unemployed
in period t is (1 + Rt+1)cst.

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