Why would one have simultaneously debt and savings? We covered previously why people have simultaneously a savings acocunt and credit card debt, in which case it is perfectly rational. Can there another case be made for rationality?
Karna Basu claim that if you know you are time-inconsistent and want to do something about it, you can set up a scheme whereby you save your wealth and then borrow when investment opportunities arise. How would this make sense? The goal is to prevent over-consumption. To do this, you need some commitment device, and in this case it is unsafe lending. People save, but because of the uncertainty about losing their holdings, their are penalized when they fail to invest. This disciplines future selves. Indeed, one could simply indulge on current consumption using the loan. However, because this is borrowed, and savings may be lost, it is too risky to be caught bankrupt next period, and one limits one's consumption. Without the risk on the savings, nothing would prevent one from over-consuming. Thus, the risk on savings is beneficial. A subtle and counterintuitive conclusion.