Figure 1: Input-Output Matrix
profits that arise in equilibrium belong to the old. Moreover, it is assumed that
in equilibrium there is no trade in profit shares.
The income of young agents comes from labor supply and is equal to the
wage income, given by,
yι,t = wt. (6)
The income of old agents comes from three sources. Recall that savings take
the form of physical capital. Therefore, old agents can sell the capital stock that
they own, the capital stock they acquired the period before net of depreciation.
In addition, they can rent out their capital and receive the return on it. Finally,
old agents receive equilibrium profits. The income of the old is given by,
y2,t = (1 — δ) Pt kt + rt kt + ∏t, (7)
where p( denotes the equilibrium price of a unit of physical capital, δ the rate
of depreciation of physical capital, rt the rental costs, and πt denotes the equi-
librium profits.
3 Equilibrium
The equilibrium involves several aspects. There are standard intratemporal
and intertemporal considerations of the consumer problem and the producer
problem. In addition, equilibrium comprises the process of selection expectation
formation technology.