It is called imperialism.
sphere of influence
American economic control of world markets
Political domination is an explicit or tacit measures taken which put a group or groups of people under the political, and sometimes, economic control of another group or groups. (Emefiena Ezeani)
Sphere of influence
; The policy or practice of intervening, especially: # The policy of intervening in the affairs of another sovereign state. # The use of government power to control or influence domestic economic activity.
I believe it is better to say 'politico-economic system', as a single wording or separately as 'political and economic systems'. They both mean thesame thing, and infer that there is a strong interchange between the political system (with institutions & Politicians as actors) and the economic system (with corporations & businessmen as actors). In this situation, those who have political powers control the economic system, and those who have economic power influences or control the political system.
Politics deals with how to govern or control, to manage public affairs. Economics discusses economic policy. It takes a government to govern and to control, but it is the government to execute its economic policy.
Imperialism
Is a political submission of a nation or state which is constituted by law and has substantial control of local affairs.
democratic system
Imperialism is the domination by a country of the political, economic and cultural life of another country. This is an unequal territorial situation. Based on a dominant militaristic attitude and feeling of superiority, in proceeds to put the control of one state over the country and people of another.
the cabinate