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Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky lifetime. We show that, under general conditions, including a perfect annuity market with actuarially fair return, imposing the optimum fertility rate and the optimum survival rate leads the competitive economy to the optimum steady-state. That Extended Serendipity Theorem is also shown to hold in economies where old adults work some fraction of the old-age, whatever the retirement age is fixed or chosen by the agents. ; Introduit par Samuelson (1975), le Serendipity Theorem énonce qu'une économie concurrentielle convergera vers son état stationnaire optimal à condition que le taux de natalité optimal soit imposé. Ce papier a pour but d'explorer si le Serendipity Theorem demeure valide dans une économie où la longueur de vie est sujette au risque. Nous montrons que, sous des conditions générales, incluant un marché d'annuités parfait offrant des rendements actuariellement justes, imposer le taux de natalité optimal et le taux de survie optimal mène l'économie concurrentielle à l'état stationnaire optimal. Il est démontré que ce Serendipity Theorem étendu reste valide lorsque les agents seniors travaillent une certaine fraction de leur temps, que l'âge de départ à la retraite soit fixé ou choisi par les agents eux-mêmes.

Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky lifetime. We show that, under general conditions, including a perfect annuity market with actuarially fair return, imposing the optimum fertility rate and the optimum survival rate leads the competitive economy to the optimum steady-state. That Extended Serendipity Theorem is also shown to hold in economies where old adults work some fraction of the old-age, whatever the retirement age is fixed or chosen by the agents. ; Introduit par Samuelson (1975), le Serendipity Theorem énonce qu'une économie concurrentielle convergera vers son état stationnaire optimal à condition que le taux de natalité optimal soit imposé. Ce papier a pour but d'explorer si le Serendipity Theorem demeure valide dans une économie où la longueur de vie est sujette au risque. Nous montrons que, sous des conditions générales, incluant un marché d'annuités parfait offrant des rendements actuariellement justes, imposer le taux de natalité optimal et le taux de survie optimal mène l'économie concurrentielle à l'état stationnaire optimal. Il est démontré que ce Serendipity Theorem étendu reste valide lorsque les agents seniors travaillent une certaine fraction de leur temps, que l'âge de départ à la retraite soit fixé ou choisi par les agents eux-mêmes.

Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky lifetime. We show that, under general conditions, including a perfect annuity market with actuarially fair return, imposing the optimum fertility rate and the optimum survival rate leads the competitive economy to the optimum steady-state. That Extended Serendipity Theorem is also shown to hold in economies where old adults work some fraction of the old-age, whatever the retirement age is fixed or chosen by the agents. ; Introduit par Samuelson (1975), le Serendipity Theorem énonce qu'une économie concurrentielle convergera vers son état stationnaire optimal à condition que le taux de natalité optimal soit imposé. Ce papier a pour but d'explorer si le Serendipity Theorem demeure valide dans une économie où la longueur de vie est sujette au risque. Nous montrons que, sous des conditions générales, incluant un marché d'annuités parfait offrant des rendements actuariellement justes, imposer le taux de natalité optimal et le taux de survie optimal mène l'économie concurrentielle à l'état stationnaire optimal. Il est démontré que ce Serendipity Theorem étendu reste valide lorsque les agents seniors travaillent une certaine fraction de leur temps, que l'âge de départ à la retraite soit fixé ou choisi par les agents eux-mêmes.

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We study the retirement decision in an economy with risky lifetime, and compare the laissez-faire with egalitarian social optima. We consider two social objectives: (1) the maximin on expected lifetime welfare (ex ante), allowing for a compensation for unequal life expectancies; (2) the maximin on realized lifetime welfare (ex post), allowing for a compensation for unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles, as well as raising the retirement age, unlike the ex ante egalitarian optimum. This result is robust to the introduction of unequal life expectancies and unequal productivities. Hence, the postponement of the retirement age can, quite surprisingly, be defended on egalitarian grounds --although the conclusion is reversed when mortality strikes only after retirement.

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We study the retirement decision in an economy with risky lifetime, and compare the laissez-faire with egalitarian social optima. We consider two social objectives: (1) the maximin on expected lifetime welfare (ex ante), allowing for a compensation for unequal life expectancies; (2) the maximin on realized lifetime welfare (ex post), allowing for a compensation for unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles, as well as raising the retirement age, unlike the ex ante egalitarian optimum. This result is robust to the introduction of unequal life expectancies and unequal productivities. Hence, the postponement of the retirement age can, quite surprisingly, be defended on egalitarian grounds --although the conclusion is reversed when mortality strikes only after retirement.

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We study the retirement decision in an economy with risky lifetime, and compare the laissez-faire with egalitarian social optima. We consider two social objectives: (1) the maximin on expected lifetime welfare (ex ante), allowing for a compensation for unequal life expectancies; (2) the maximin on realized lifetime welfare (ex post), allowing for a compensation for unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles, as well as raising the retirement age, unlike the ex ante egalitarian optimum. This result is robust to the introduction of unequal life expectancies and unequal productivities. Hence, the postponement of the retirement age can, quite surprisingly, be defended on egalitarian grounds --although the conclusion is reversed when mortality strikes only after retirement.

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We study the retirement decision in an economy with risky lifetime, and compare the laissez-faire with egalitarian social optima. We consider two social objectives: (1) the maximin on expected lifetime welfare (ex ante), allowing for a compensation for unequal life expectancies; (2) the maximin on realized lifetime welfare (ex post), allowing for a compensation for unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles, as well as raising the retirement age, unlike the ex ante egalitarian optimum. This result is robust to the introduction of unequal life expectancies and unequal productivities. Hence, the postponement of the retirement age can, quite surprisingly, be defended on egalitarian grounds --although the conclusion is reversed when mortality strikes only after retirement.

A premature death unexpectedly brings a life and a career to their end, leading to substantial welfare losses. We study the retirement decision in an economy with risky lifetime, and compare the laissez-faire with egalitarian social optima. We consider two social objectives: (1) the maximin on expected lifetime welfare (ex ante), allowing for a compensation for unequal life expectancies; (2) the maximin on realized lifetime welfare (ex post), allowing for a compensation for unequal lifetimes. The latter optimum involves, in general, decreasing lifetime consumption profiles, as well as raising the retirement age, unlike the ex ante egalitarian optimum. This result is robust to the introduction of unequal life expectancies and unequal productivities. Hence, the postponement of the retirement age can, quite surprisingly, be defended on egalitarian grounds --although the conclusion is reversed when mortality strikes only after retirement.