Retirement incomes: Private savings versus social transfers

It has long been known, from the work of Samuelson and Aaron, that if(appro ximately) the sum of the population and real earnings growth rates exceeds the real interest rate, all individuals can be made better off by using a p ay-as-you-go pension scheme. The basic overlapping generations model that i s typically used to examine such intergenerational transfers makes no allow ance for labour supply responses to taxes and transfers, and so cannot be u sed to examine optimal tax and pension levels. The present paper allows for labour supply effects, whereby a tax imposed to finance current pensions i ntroduces distortions to labour supply and a reduction in the tax base. The optimal proportional tax rate, and therefore the optimal combination of pr ivate savings and social transfers, is derived in terms of the time prefere nce rate, the taste for leisure, real interest and productivity and populat ion growth rates. It is found that the condition under which the optimal ta x is positive is the same as the Samuelson-Aaron condition. A crucial ingre dient in obtaining this result is an assumption that pension levels are adj usted in line with the growth of wage rates rather than, for example, being held constant in real terms. This in turn is found to imply that earnings grow at the same rate as the wage, so long as preferences are such that lei sure can be expressed as a proportion of full income.