The concept of a semiflexible functional form is applied to the Almost
Ideal (AI) demand system. This yields a demand model that is more par
simonious than standard ones while preserving a degree of flexibility,
that satisfies the curvature property of concavity of the underlying
expenditure function (at least locally), and that preserves the desira
ble properties of the Al model (aggregation across consumers and nonli
nearity of the Engel curves). The model is illustrated with an applica
tion to a relatively large demand system emphasizing food consumption.
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