The Taxation of Saving Returns in Overlapping Generations Economies with Stochastic Asset Bubbles

In the standard simple overlapping generations model with production (Diamond (1965)), the steady state competitive equilibrium level of capital under laissez-faire does not typically maximize the net production if the agents can save only in terms of capital. In particular, whenever the steady state competitive equilibrium level of capital is too high, net production and consumption can be increased withdrawing resources from the production process by means of a mechanism —such as fiat money as in Tirole (1985), or a rolled-over public debt as in Diamond (1965)— allowing to transfer savings from the young to the contemporaneous old in order to be consumed. Any such mechanism is essentially based on the agents’ certainty that their future claims obtained in exchange of their participation in the mechanism will be honored (by the next generation, by the government,...), i.e. that such claims will have some value. Nevertheless, the actual decentralization of the best possible steady state as a competitive equilibrium by means of, say, fiat money is undermined by the fact that, at that steady state, the agents’ demand for money is indeterminate when this same money is known to be valued for sure next period, since then the return to this alternative channel of savings has to be equal to the return to capital at the steady state. Nevertheless, this indeterminacy disappears as soon as there is some chance (no matter how small) that the money (or debt) being offered may be repudiated next period. Weil (1987) showed that competitive equilibria in which money may lose its value (stochastic bubbles) do exist as long as the probability of this happening is small enough. In this paper I show (i) firstly, that the best steady state attainable by means of such ”risky” money is not a competitive outcome under laissez-faire; and (ii) secondly, that this best steady state with ”risky” money is nonetheless attainable as a competitive outcome if returns to capital savings (but not returns to monetary savings) are taxed adequately and the amount raised returned to the same agents as a lump-sum transfer.