Abstract: We estimate a semi-nonparametric demand system based on a multivariate version of the Muntz-Szatz series expansion which is called the Asymptotically Ideal Model (AIM). The model is applied to consumer demand for dried fruits, raisins, and dried plums. Results from the first and second order AIM expansions suggest that the second order expansion leads to a more economically consistent model, but the likelihood ratio test indicates the AIM(2) model was not a statistical improvement over the AIM(1) model.