When a number of countries agree to remove all trade barriers among themselves and at the same time charge a common tariff against non member countries, it ...

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The option that describes a situation where a number of countries agree to remove all trade barriers among themselves and charge a common tariff against non-member countries is called a "customs union." A customs union is a group of countries that agree to remove trade barriers such as tariffs, quotas, and other restrictions on goods and services traded between themselves. In addition, they establish a common external tariff, which means they all charge the same tariff on goods imported from countries outside the union. This allows the member countries to promote trade among themselves while protecting their economies from external competition. Therefore, in a customs union, members eliminate trade barriers between themselves while imposing a common external tariff on non-members.