We prove that for any incomplete market and any concave utilityfunction the marginal propensities to consume and to save are alwayspositive. Furthermore, we introduce a class of incomplete markets thatincludes almost all well known examples of market incompleteness infinance and macroeconomics. Two concrete examples are idiosyncraticincome shocks and general, diffusion driven incompleteness. For allmarkets in our class we explicitly solve the associated utility maximizationproblem by a recursive construction and derive many importantproperties. For example, precautionary savings and the diminishingmarginal propensity to consume. Effectively, the class is characterizedby these two economic properties.[...]