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...

The problem faced here by a firm whose input quantities are fluctuating is to choose the optimal combination of average input quantities so as to maximize expected revenue under a cost constraint. We show that for the prevailing production functions, the firm might find it optimal to increase...