A new model of consumer preferences is introduced. It is appropriate for modeling perishable commodities which are produced with a lag, where it is reasonable to assume the market-level quantities are fixed by previously made production decisions. The inverse Lewbel system, as it is called, is a flexible nonlinear system of share equations, which nests two other inverse demand systems, the direct translog and the inverse AIDS. Thus, the inverse Lewbel may be employed to test whether these more restrictive preference structures are appropriate. In an application to quarterly U.S. meat consumption, the more restrictive structures are rejected.