In consumer theory, each good and its price may be considered conjugate. However, it is not clear which good is conjugate to the budget, or which dual variable is conjugate to the numeraire once the system has been normalized. In this paper we show that if the consumption space is the strictly positive orthant in n-space and the consumer is never satiated, then there is an open unbounded set on which the budget can replace the numeraire as the independant variable of an inverse demand system. Although it would be nice to be able to replace 'unbounded' by 'dense' (since then the complementary set would be a null set) we give counterexamples in which either consumption space is not the full positive orthant in Rⁿ or preferences exhibit satiation.