Envy today, inequality tomorrow: how present bias shapes the wealth distribution

We study the effects of envy (relative consumption concerns), drawing on evidence that preferences typically exhibit present bias. We employ a Ramseytype model with agents who differ in initial capital endowments and account for present-biased envy: agents are naive and care about how their consumption levels compare to those of others only in the current period. Presentbiased envy, unlike permanent envy, significantly affects both the level of inequality and the aggregate income level in an economy. First, it generates the Matthew effect (the relatively rich get richer while the relatively poor get poorer), and after a finite time, only the initially wealthiest agents own the entire capital stock and the debts of others who are in the maximum borrowing state. Second, in contrast to both an economy without envy or with permanent envy, present-biased envy makes agents effectively more impatient, reducing the long-run capital stock and aggregate income level.