| Sumario: | Our objective has been to test the theory of demand without imposing the assumptions of additivity and homotheticity as part of the maintained hypothesis. For either the direct or the indirect series of tests, we conclude that the theory of demand is inconsistent with the evidence. These results confirm the findings of Wold (in association with Lars Juréen) for the double logarithmic demand system and Barten for the Rotterdam demand system. At the same time our results provide the basis for more specific conclusions. If the theory of demand were valid, the double logarithmic form for the system of demand functions would imply that the utility function is linear logarithmic. Similarly, the validity of the theory of demand and the Rotterdam form for the system of demand functions would imply linear logarithmic utility. An equally valid interpretation of the results of Wold and Barten is that the theory of demand is valid, but that utility is not linear logarithmic. Our results rule out this alternative interpretation and make possible an unambiguous rejection of the theory of demand. A possible alternative to our test procedure is to maintain the validity of the theory of demand. Proceeding conditionally on the validity of demand theory, we would reject the hypothesis of additivity for the direct series of tests. Additivity of the direct utility function is employed as a maintained hypothesis by Houthakker in the direct addilog demand system, by Stone in the linear expenditure system, and by Basmann, Johansen, and Sato in the demand system incorporating features of both. Again, proceeding conditionally on the validity of the theory of demand, we would accept the hypothesis of additivity for the indirect series of tests. This hypothesis is maintained by Houthakker in the implementation of the indirect addilog demand system.
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