This study analyzes quantity impacts of imported crawfish tailmeat on Louisiana crawfish tailmeat prices, and demonstrates the statistical validity and proper interpretation of cross substitution within inverse demand systems. Among five inverse demand systems, the Differential Inverse National Bureau of Research (DINBR) model shows no violation of econometric assumptions for the data analyzed. By using Allais coefficients proposed by Barten and Bettendorf (1989), we show substitutability among the five fish species.