Why would a department that is traditionally focused on domestic issues become involved in foreign policy-making

A department that is traditionally focused on domestic issues could become involved in foreign policy-making because of two main reasons:

It can regulate a good or service given internationally. For example, it can be clothes or technological devices. Foreign policy-making (or foreign relations), also regulates behavior that could have an international consequence. For example, it could be a business that contaminates the environment.

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