My paper “A Theory of the Saving Rate of the Rich” was accepted at Journal of Economic Theory. I started this project in early 2020. Initially, the paper was about rigorously establishing the asymptotic linearity of policy functions when preferences are homothetic and the constraint is asymptotically homogeneous of degree 1. This is not surprising but the proof is difficult. As we worked on the proof, we (my coauthor and I) discovered that the asymptotic slope of the policy function can be zero, which was surprising. When the asymptotic marginal propensity to consume (MPC) is zero, an infinitely wealthy agent saves 100% of the wealth, which can explain the empirical puzzle that wealthy people save a lot although it seems unnecessary. So instead of focusing on just a mathematical fact, we decided to frame the paper as a new theory of the saving rate of the rich.
Some economists make a big deal about non-homothetic preferences to explain the high saving rate of the rich. According to our theory, non-homotheticity is unnecessary. It is nice to have an intuition, but sometimes the intuition is incorrect, as in this case where homotheticity can generate zero asymptotic MPCs. This is a good example that any theoretical argument should be based on theorems and proofs, and not on intuition.