## Abstract

The article reconsiders the implications of the choice of pure social time preference for intergenerational equity in the presence of a time-consistent utilitarian social welfare criterion. The analytic framework is a setting with overlapping generations, lifetime uncertainty, population growth and technical progress. The analysis identifies upper and lower bounds for the feasible range of social discount rates and draws a corresponding distinction between “gerontocratic” and “Stalinist” optimal plans. The paper corrects a number of inaccurate propositions in a related earlier contribution by Marini and Scaramozzino (2000) to this journal.

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## Notes

## References

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## Acknowledgements

Helpful comments by an anonymous referee and an associate editor are gratefully acknowledged.

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*Responsible editor:* Alessandro Cigno

## Appendix

### Appendix

### Derivation of the indirect utility function *U*(*c*) when felicity is iso-elastic

It is assumed that the felicity function *u*(.) in Eq. (1) takes the iso-elastic form

Evans (2005) provides empirical support for the assumption of a constant elasticity of marginal utility *θ*=1/*σ*. Integration of Eq. (8) from *t*−*h* to *t* yields

Inserting (A-2) into the intratemporal consumption constraint, one obtains

provided that *β*>*σ*(*δ*−*ρ*). If this inequality—which is equivalent to condition (19) in the main text and implies an upper limit for the feasible range of *δ*—does not hold, the intratemporal consumption allocation rule (8) is not consistent with the intratemporal resource constraint (5) and an optimal plan does not exist for the chosen social discount rate. Combining (A-2) and (A-3), one finds

which is equivalent to (20) in the main text. As *U*(*c*) in Eq. (9) is by definition equal to the inner integral of Eq. (3), its functional form is found by inserting (A-4) into

and, hence,

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### Cite this article

Willenbockel, D. Social time preference revisited.
*J Popul Econ* **21**, 609–622 (2008). https://doi.org/10.1007/s00148-006-0073-z

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DOI: https://doi.org/10.1007/s00148-006-0073-z

### Keywords

- Intergenerational equity
- Overlapping generations
- Social discount rate

### JEL Classification

- H43
- E13
- O41