A Model of Indivisible Consumption Categories

We offer a model that adapts the classical consumer choice model by assuming the indivisibility of consumption categories. Specifically, we assume that most consumption categories have a minimal expenditure threshold. This seems plausible with reference to real life (e.g., consumption related to car-ownership, or consumption related to buying a house). Our model provides a novel explanation for two puzzles: (1) why people often buy both insurance and lottery tickets, (2) why people often behave in a way consistent with narrow framing of their situation rather than acting out of global principles of maximization. We show that the complexity level of the consumer problem is non-monotonic and relatively small for low wealth NP-hard for medium wealth and polynomial for high enough wealth. Next, we show that the model induces decreasing absolute risk aversion in wealth. we also show that investing in a lottery ticket (i.e., a product with high gain - small loss) can be worthwhile for those with low wealth and for a medium wealth the added value of the lottery decreases down to a negative value as wealth increases Finally, we show that for significant loss/gain the model induce the fourfold pattern of risk attitude: small probability inducing risk aversion for loss and risk loving for gain and high probability inducing risk loving for loss and risk aversion for gain.