Optimal Sequence of Inter-Generational Borrowing and Lending Leading to Escape from the Poverty Trap through an Invisible Hand

The overlapping generations (OLG) model of micro-based macroeconomics has been utilized in order to calculate the optimal sequence of inter-generational transfer payments and evaluate its effects on the operation of an economy which suffers from the poverty trap. Each generation has been assumed to live for two periods and aims to find the optimal relationship between its borrowing from the previous generation and its lending to the next generation so that its discounted utility function is maximized. This optimization is subjected to budget constraints, the competitiveness of labor and capital markets and the equilibrium condition of savings and capital. Individuals in all of the generations are assumed to pay no attention to the utility level of the next generation (i.e. they do not have altruism). Furthermore, government limits the domain of choices of the generations with the additional constraint that the borrowing and lending amounts of each generation should be positively correlated. Each generation, when it compares its discounted utility levels corresponding to the two options – i.e. participation in the payment system or not, assuming perfect information – understands that participation in the system is beneficial and thus wishes to share in the payments system. This participation consists of two parts, one is borrowing when young (saving together with consuming), and the other is lending when old (consuming only). A moral hazard may thus occur due to the fact that the young generation after borrowing decides not to pay its share back to the new young generation when it becomes old. Thus, the government is also necessary in order to prevent this moral hazard. However, no special objective function of the government enters the problem formulation. It is observed that, as an important side effect, the sequence of transfer payments obtained can not only bring the economy out of the poverty trap, but it also raises the stable equilibrium level of the capital-labor ratio to a level higher than that is achievable by a comparable competitive economy without transfer payments. The steady-state obtained has another advantage over the competitive equilibrium, viz., such an improved equilibrium is dynamically efficient and in this equilibrium the economy would operate within the golden rule situation. These side effects, which are the benefits received by the whole economy as a result of the decisions made by selfish generations, seem to be inter-generational interpretations of the Invisible Hand concept of Adam Smith.