Integrability of incomplete demand systems is discussed. The concepts of weak integrability, quasi-expenditure function, quasi-indirect utility function, and quasi-utility function are defined. Their relationships to the expenditure function, indirect utility function, and utility function are developed. The dual structure of the quasi-functions permits exact welfare analysis and reveals the conditional preference structure for the commodities of interest. New results relating the uniqueness and exactness of consumer's surplus to the structure of the expenditure and indirect utility functions are obtained.
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