Dumping and antidumping are among the prominent issues in trade negotiations these days. All economists agree that any barrier to the free flow of goods among countries of the world is welfare reducing. However, the proponents of antidumping laws claim that these laws are not meant to limit free trade but to promote fair trade, and therefore, if the trade is fair in laissez-faire environments, which in this case implies that dumping does not occur in the absence of antidumping law, the introduction of antidumping laws should not matter;The definition of dumping commonly used in antidumping cases is that dumping is considered to have occurred if the price charged by a firm in a foreign market inclusive of transportation costs is lower than the price that firm charges for the same product in a domestic market. In these circumstances the antidumping law recommends that tariff, which is some proportion of the difference in the two prices, be imposed on the imports. We use best response curves in a simple duopoly model and analyze the effects of antidumping laws. We show that this type of tariff rule gives an edge to the home (importing) firm over the foreign (exporting) firm and creates non-concavity in the home firm's profit function, and this causes jumps in its best response curve. While solving the model we show that multiple local solutions may exist due to the unique structure of the home firm's best response curve. When solutions are hard to characterize analytically, we use numeric simulation. We simulate a situation where, in the absence of antidumping law, dumping does not take place in equilibrium. However, if the antidumping law is introduced in this situation, multiple solutions emerge some of which are in the regions where the law is actually binding for the foreign firm;Intuitively, one expects that the antidumping laws would not affect decisions of the firms in both importing and exporting countries if the dumping does not occur in laissez-faire situation. However, we demonstrate that the presence of antidumping laws can lead firms to modify their behavior.