In establishing the validity of discrete choice models for economic analysis, a fundamental issue is whether or not they adhere to the integrability conditions. These conditions ensure that, for any system of demand functions involving a symmetric negative semi-definite substitution matrix, there necessarily exists an underlying utility function from which the demandfunctions can be derived. Conventionally, the integrability conditions exploit 'continuous' demand theory, wherein preferences are defined on a continuous commodity space. Indeed the conditions are based on the partial derivatives of Hicksian demand functions with respect to price and income, and thus appeal to smooth and continuous demand functions. Discrete choice models may be seen as special case of continuous demand theory, such that choice is restricted to a finite and exhaustive subset of the commodity space, and this provokes some challenges in translating the conventional integrability conditions. The study considers a more general, and therefore flexible, model of consumption, arising from the combination of both discrete and continuous choices. In particular, this model is applied to the dual theorem of demand, establishing the integrability conditions applying separately to the discrete and continuous consumptions. For the covering abstract see ITRD E146031
Samenvatting