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 beenutilized in order to calculate the optimal sequence of inter-generationaltransfer payments and evaluate its effects on the operation of an economywhich suffers from the poverty trap. Each generation has been assumed to livefor two periods and aims to find the optimal relationship between itsborrowing from the previous generation and its lending to the next generationso that its discounted utility function is maximized. This optimization issubjected to budget constraints, the competitiveness of labor and capitalmarkets and the equilibrium condition of savings and capital. Individuals inall of the generations are assumed to pay no attention to the utility levelof the next generation (i.e. they do not have altruism). Furthermore,government limits the domain of choices of the generations with the additionalconstraint that the borrowing and lending amounts of each generation shouldbe positively correlated. Each generation, when it compares its discountedutility levels corresponding to the two options – i.e. participation inthe payment system or not, assuming perfect information – understandsthat participation in the system is beneficial and thus wishes to share in thepayments system. This participation consists of two parts, one is borrowingwhen 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 younggeneration after borrowing decides not to pay its share back to the new younggeneration when it becomes old. Thus, the government is also necessary inorder to prevent this moral hazard. However, no special objective function ofthe government enters the problem formulation. It is observed that, as animportant side effect, the sequence of transfer payments obtained can not onlybring the economy out of the poverty trap, but it also raises the stableequilibrium level of the capital-labor ratio to a level higher than that isachievable by a comparable competitive economy without transfer payments. Thesteady-state obtained has another advantage over the competitive equilibrium,viz., such an improved equilibrium is dynamically efficient and in thisequilibrium the economy would operate within the golden rule situation. Theseside effects, which are the benefits received by the whole economy as a resultof the decisions made by selfish generations, seem to be inter-generationalinterpretations of the Invisible Hand concept of Adam Smith.