The efficiency of large(r) endowments: the optimal endowment is bigger than you might think

ABSTRACT

This study argues that endowments can be efficient, both for a finite-lived and infinitely-lived agent. When the lost utility from forgone consumption is less than the discounted utility brought by the cash flows paid throughout the endowment, endowments are utility-enhancing. Given that this can be utility enhancing for a finite-lived person, the direct connection can be made to an infinitely-lived agent who would receive utility enhancement through an endowment, such as a university. Given the recent political push to force well-endowed universities to spend down their endowments, displaying how an endowment’s existence can be efficient is important for policy-makers.

KEYWORDS:

• Personal endowments
• non-profit endowments
• university endowments
• Utility

JEL CLASSIFICATION:

• I28
• D90
• H41

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ I use endowment as the funds functioning as endowments (see Ehrenberg 2009).

² This is modelled with a one period savings example, i.e. save everything needed during the first time period (year of work) then no more savings needed. See Merton (1971) for the analysis of utility maximizing over multiple years. However, it is possible that one large savings rate, which decreases over time, is utility-maximizing. This paper presents an extreme example of this and leaves the optimal savings path for future research. A simple numerical example is in the appendix.

³ From the Social Security website: https://www.ssa.gov/oact/cola/awidevelop.html.

⁴ Since the 1977 inception of the 30 year treasury note the average return on this note has been 6.8%. Even when dropping all months above 10%, the average is still well above 5% – at 5.9%. Although our current times have a low yield, the use of 5% for a risk-free return is accurate when using historical data.