On Some Missing Equations in Contemporary Treatments of Intertemporal General Equilibrium

Area 13 – Scienze economiche e statistiche

It has not been sufficiently noticed that in an Intertemporal general equilibrium system as many Walras’s laws underlie the equations as there are dates in the system, with the implication that an equivalent number of equations are not in fact independent. This has been hidden from view by the fact that an equal number of equations which had as much title to be included as the remaining ones have been omitted. These missing equations are those concerning savings and investment in each period of the life of the economy. Thus, when the system is correctly written, such equations emerge as a part of the system as essential, or inessential, as e.g. the equations concerning the demand and supply of labour for the same dates – i.e. as much independent of, or dependent on, the remaining equations as those labour equations. The two associated shortcomings – i.e. the oversight of the dated Walras’s laws and that of the dated savings and investment equations – compensate each other with respect to a merely formal view of the determinacy of the system, and are in fact likely to have seriously affected the analysis of its properties by leading the interpreter to ignoring the capital goods yearly indirectly demanded by the individuals as savers through the firms – a demand which obeys principles very different from those governing their demand for consumptions goods.

SINTESI