How did the production of tobacco and sugar in Britain's colonies affect the prices of these products in Europe and the Americas in the eighteenth century?

The production of tobacco and sugar in Britain's colonies increased their supply. This increase in their supply reduced their prices.

Explanation:

This is simply an application of the law of demand and supply.

The law of demand states that the quantity of demanded good reduces as the prices increases. The law of supply states that the quantity of goods supplied increases as the prices increases and vice-versa.

In general, low supply and high demand increase price while high supply and low demand reduces prices.

When Britain's colonies began to produce tobacco and sugar, this drastically reduced their demand in Europe and the Americas and this affected the prices and reduced it.