Theory doesn't tell you what impact more liberal trading rules will have on public health.
Lower tariff and non-tariff barriers to trade may reduce the cost and increase the variety and quality of available health related goods and services. Increased average incomes may increase the demand for those goods and services. Ideas and best practice may spread with trade. If trade creates profit opportunities, and stimulates investment and growth, it may contribute to increased incomes and increased demand for private and public health goods. Increased foreign investments by multinationals may be associated with better working conditions.