The analysis of this paper was originated by Brander and Spencer (1985) who proposed a three-country and one commodity model that two countries compete the commodity share in a third country market. They argued in their analysis that export subsidies enhance the country welfare, and supported trade under strategic trade policies rather than free trade. Mai and Hwang (1989) considered the Brander and Spencer model but with a labour-managed firm in one country and concluded that export tariffs are effective in order to raise the social welfare of a labour-managed country. Then, our next and interesting task is to investigate what sort of policies is effective if both countries are labour-managed. We will focus on this topic. Being different from the previous works of Brander and Spencer (1985) and Mai and Hwang (1989), it will be shown that the optimal trade policy is not uniquely determined. Which is optimal between an export subsidy and export tariff relies on the relation of the slope of the foreign reaction curve to that of the home isowelfare curve.