Why does poverty increase time discounting? A mathematical model

People in situations of poverty tend to heavily discount the future. Despite robust evidence, the theoretical literature lacks satisfying models to explain why. Existing theories often invoke urgent needs to explain impatience, this intuition is not sufficient: in persistent poverty, one may need resources tomorrow as much as today. We show that previous models assume that poverty is temporary and improvement is expected, and predict discounting only under this condition, which is rarely realistic. Here, we present the first model showing that time discounting can be rational in persistent poverty. We propose a two-period model in which basic needs are captured by a 'desperation threshold' -- a critical resource level above which agents aim to stay. In four stylized scenarios, we show analytically that agents discount the future near the threshold and are patient at intermediate resource levels. In line with the empirical record, time discounting increases on both sides of the threshold, while risk taking is polarized -- higher below the threshold, lower above. Unlike existing accounts, our explanation does not rely on assuming a future improvement in financial situation. Rather, it predicts a U-shaped effect of future expectations, with greater time discounting if the future will be either much better or much worse than the present, which can reconcile economic theory with ethnographic findings. Our findings suggest that addressing material scarcity directly, rather than attempting to alter future orientation, may be the most effective way to reduce time discounting and align behavior with true preferences.