The multiplier effect is used to describe the effect that government spending has on an economy not the national debt increasing.
The multiplier aims to show how much the GDP of the country would increase by given an increase in government spending. It is calculated by the formula:
= 1 / (1 - Marginal Propensity to Consume)
Assuming this multiple is 5 for instance, if the U.S. government increased spending by $5 billion, GDP would be expected to increase by:
Some slaves bought their own freedom from their owners, but this process became more and more rare as the 1800s progressed. Many slaves became free through manumission, the voluntary emancipation of a slave by a slave owner.