Optimal trade and industrial policies are examined in an export-rivalry and a home-market model with general cost heterogeneity among firms. The roles of the demand and cost structures in policy determination are systematically analysed. It is shown that the equal-markup property holds in both models under the firm-specific industrial policy. A more efficient firm has a higher subsidy or a lower tax rate than an inefficient one. In the home market model under free trade, the firm-specific industrial policy always calls for subsidies to all home firms. Under the firm-specific trade policy, it is shown that the difference between any two tariff rates exactly equals 100% of the difference between the foreign firms' marginal costs, the home industry is always granted some positive level of protection, and a production-tax-cum-import-subsidy policy is never optimal.