Discrete/continuous models of consumer demand with binding nonnegativity constraints

Consumers in this model are assumed to maximize utility with respect to two goods, one of which is available in several alternative forms. Decision rules of consumers are derived for two cases concerning this good: (a) either the individual chooses one of the available alternatives or (b) the individual chooses to altogether forgo its consumption. Choice probabilities, the demand equations, and the zero-consumption probability are derived and reflect the interrelatedness of the discrete/continuous choices and the binding nonnegativity constraint. We show that the traditional discrete/continuous choice models yield estimates of demand which are biased and choice probabilities which are also biased, except in a special circumstance.