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Tariff literature on third-degre price discrimination remains only lightlyexplored. The purpose of the paper is to investigate whether there exist optimumtariffs in the presence of different demand elasticities. We explore (i) the case ofoptimum uniform ad valorem tariff, and (ii) the case of optimum discriminatory advalorem tariffs. A two-stage optimization approach is used: profit is maximized fora foreign firm in the first stage and importing country’s optimum tariff rates aredetermined under maximization of welfare (sum of consumer surplus and tariffrevenue). The result indicates that the optimum tariffs may not exist even with a setIn Search of the Optimum Tariffs Under~ 19of well-behaved linear demand functions. Consequently, computer simulations areneeded with cost and demand parameters to ensure better welfare position forhome country.JEL classifications: F10, F12