Optimal Consumption Policy under Uncertain Income

This paper considers the consumption behavior of a risk-averse consumer with a preference for immediate consumption who faces an uncertain income stream and plans for a finite or infinite number of periods. The consumer may borrow up to a limit or save, where both saving and borrowing are subject to the same positive rate of interest. We derive the optimal consumption policies for both finite and infinite planning horizons, investigate their characteristics, and analyze their economic and behavioral implications.