This paper compares the steady-state and dynamic outcomes of two historical alternatives as a means of old-age insurance, namely, voluntary intra-family transfers from young to old members versus pay-as-you-go public pensions, in a general equilibrium overlapping generations model with children as a desirable good. We show that the shift from a private system of old-age support to public pensions increases the gross domestic product (GDP) per worker. Moreover, although in both cases the steady-state stock of capital, under myopic expectations, may be (globally) unstable depending on the size of the inter-generational transfer, we show that the existence of public pensions rather than private intra-family gifts considerably reduces the possibility of cyclical instability
