We present a third‐market model with a vertical trading structure, in which upstream input suppliers engage in homogeneous price competition. We show that, under downstream Bertrand competition, a non‐monotonic export policy may result. Specifically, the optimal policy of the exporting country can turn into a tax–subsidy–tax as the degree of product substitutability rises. We also confirm the conventional result for which the optimal policy is an export subsidy (tax) if there is Cournot (Bertrand) competition downstream, provided that the number of domestic suppliers is at an intermediate level. We further discuss bilateral policy interventions when both exporting countries offer a subsidy/tax to their domestic downstream firms. We show that a non‐monotonic export policy (tax–subsidy–tax) can arise even in this extended setting.