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Based on the concept of weakly separable utility (which applied empirical work implicitly or explicitly assumes), this paper develops a theoretical condition that a set of own and cross-elasticity of demand estimates must satisfy. The paper shows how the condition may be used to evaluate or calculate estimates of cross-elasticities of demand. The condition is illustrated for the constant elasticity of substitution utility function.  Finally, it is applied to the problem of estimating the effects of the US and EC extensive system of voluntary export restraints on world steel trade. Through its use, perverse results are avoided.