On the Existence of Endogenous Cycles
Endogenous business cycles have been known to exist in the overlapping-generations model since quite a long time. The literature seems to imply that these cycles may exist only if individuals show rates of preference for the present that are high enough, and these values have to be so high that they are unrealistic. While this observation is true if preferences are homothetic, we show in this paper that, once the homotheticity requirement is dropped, a sufficient condition for the existence of cycles is that the Engel curve defined for equal prices (therefore taken equal to one) has at least a point where the slope is smaller than one. This condition expresses a mild form of impatience. Given this condition, it is always possible to find a discounted utility function (for any arbitrary given discount rate smaller than one) and positive endowments such that the corresponding overlapping- generations model features cycles of order two.
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