In this paper, we examine the consequences of adopting the random utility hypothesis as an approach for randomizing a system of demand equations. Random utility models are appealing since they allow the usual assumption of deterministic utility maximizing behavior by each consumer to co-exist with the apparent randomness across individuals which is exhibited by data. Our results show that the use of random utility models implies that the disturbances of the demand equations may not be homoskedastic but must be functions of prices and/or income. If the demand system is generated by random utility maximization, then empirical studies of demand which have assumed homeskedastic disturbances will suffer the usual inferential difficulties. A possible explanation for the common rejection of demand theory axioms in applied work, therefore, is provided by the fact that most previous demand studies have, in fact, assumed homoskedasticity. A sampling experiment provides some evidence that ignoring the heteroskedasticity leads to an incorrect test size for a test of symmetry. Heteroskedastic-consistent tests are compared to the usual tests. At least one is found to work reasonably well in small samples in the presence of heteroskedasticity.