We analyze the market dynamics that are caused by tariff-rate quotas, particularly the effects of quota license allocation between heterogeneous commodities at the tariff line level. The allocation is endogenously modeled with a mixed complementarity problem approach for the case of the Comprehensive Economic and Trade Agreement between Canada and the European Union. The model results are compared both with alternative models that resemble pre-existing approaches and with the real trade figures that have been collected since the trade agreement's implementation. Our analysis shows a bias toward more expensive commodities if the shadow value of a quota license manifests in a secondary license market. The same quota can thereby be binding to some commodities but not so for others. This feature of quotas can be crucial for policymakers who are concerned about price effects or who want to understand the effects of lumping together commodities of different quality in one quota.