A universal assumption of models allocating a country's imports among suppliers is that demand is separable over foreign and domestic sources. Nearly as common are the assumptions that import demands are homothetic and mutually separable. This paper explores the theoretical implications of these assumptions and then tests them, applying Deaton and Muellbauer's `Almost Ideal Demand System¿ to U.K. data on manufactures covering 1952¿1979. It uses Lagrange Multiplier tests. Both homogeneity and separability are overwhelmingly rejected. A model of import demand without these restrictions is introduced which, while not entirely satisfactory, suggests a direction for future research
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