We present a model of international market share rivalry where the domestic export subsidy is determined by lobbying. Greater domestic cost heterogeneity leads to a higher subsidy level and a larger domestic market share. However, the relationship between cost heterogeneity and welfare is ambiguous. Starting from a near-symmetric situation, an increase in heterogeneity reduces domestic welfare if the number of domestic firms exceeds some critical value. when starting farther from symmetry, the welfare effect is reversed. Our findings are in contrast with the results from the existing literature where lobbying is ignored