Abstract
Necessary and sufficient conditions are obtained for the permanence of where E: R→R and x 0, μ ∊ R. Sufficient conditions for bounded oscillations are also obtained. This equation represents a first order realization of a discrete dynamical model of consumer demand. When there is a unique fixed point, sufficient conditions for the global asymptotic stability are obtained. Also, after defining consumer accounts, the budget identity is shown to hold asymptotically in the mean.
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