Final answer:
The British interest in establishing colonies was influenced by the economic theory of mercantilism, which aimed at amassing wealth through trade and maximizing gold and silver reserves, leading to strict control over colonial trade.
Step-by-step explanation:
The British interest in establishing colonies was influenced by the theory of mercantilism, which posited that a country's power was directly related to its wealth, particularly in gold and silver. This theory maintained that the world's wealth was a finite resource and that nations were in constant competition to acquire more of these precious metals to achieve self-sufficiency and economic dominance.
Mercantilist nations sought to increase their wealth by extracting raw materials from their colonies, especially precious metals. They implemented policies that required colonies to trade exclusively with the mother country, facilitating a favorable balance of trade. England, like other European powers, adopted mercantilism to assert control over trade, accumulate wealth, and support a strong military, thus cementing its status as a global power during the colonial period.
Despite its popularity, mercantilism faced criticism by economists like Adam Smith, who argued that wealth was not finite and that nations could simultaneously prosper without such restrictive practices. Nonetheless, mercantilism remained a guiding principle of British colonial policy throughout the seventeenth and eighteenth centuries, influencing the establishment and governance of the American colonies, as well as the Atlantic slave trade and international relations of the period.