Overlapping Generations Model (OLG)

In our models so far we had assumed that agents live infinitely, which everybody knows is unrealistic. So, in this model attempt was made to relax this assumption. Also, we try to look that if generations overlap and have to trade with one another then how will the competitive decentralized equilibrium change (if it does). This model allows for the possibility that the decentralized competitive equilibrium be different from the social planner's allocation. In fact, the competitive equilibrium may not be the Pareto optimal solution. 

Key assumptions: Time is discrete here but goes on forever. The model consists of "young" and "old" generations. Each generation lives for two periods and die. At the start of every period, the same number of identical people are born. In the beginning, however, there were two types of households, those born then and the initial old. In every period every individual receive an endowment of perishable consumption goods i.e. two units for young and one unit for old. Households can use it for consumption expenditure or hold one period bond that offers them a certain return. Also, the utility function is assumed to be concave and time separable which generates motive to consume even in the next period.

The competitive equilibrium in the OLG model is defined such that all the agents optimize their utility subject to budget constraints, prices are taken as given, bond markets clear (sum of bond holdings across all the households is zero) and goods market clear (sum of total consumption equals the sum of total endowment). So, we observe that the young generation does not trade with the old generation since the old generation would not be able to payback (Duh!). Further, since all the households are identical, so if anyone household demands a savings bond, then so will the other households. Thus no one will hold any bonds. Therefore what we observe is that the equilibrium is autarky (no trade)  and each individual simply consumes its own endowments. The analysis of Pareto optimality showed that if we can distribute the endowments from young to the older generation then the pareto optimal solution is possible, thus the competitive equilibrium without government is Pareto inefficient. 

So, we assume that government interferes and helps in this re-distribution, via fiat money (here for now). So, the central bank distributes certain fix amount of money equally amongst everyone. Now the fiat money allows the generations to interact through the trade of endowments. The young generation can sell some of their endowment for a certain fixed price to the older generation and use that money to buy some endowment in its future period. So, we see that if the young generation value the utility derived from future consumption enough then the money will hold its value and enable interaction or trade between generations. Thus, the money will allow individuals to smooth their consumption over time and yield Pareto optimal solution over inefficient autarky equilibrium.

References:

1. Advanced Macroeconomics, Overlapping generations model, StFX University, accessed on October 26th, 2018

2. Overlapping Generations Model, Advanced Monetary Economics 2018, Adam Spencer, University of Nottingham, accessed on October 26th, 2018