Suppose that throughout the U.S. economy, individuals spend...

Suppose that throughout the U.S. economy, individuals spend $$90 \%$$ of every additional dollar that they earn. Economists would say that an individual's marginal propensity to consume is 0.90 . For example, if Jane earns an additional dollar, she will spend $$0.9(1)=\$ 0.90$$ of it. The individual who earns $$\$ 0.90$$ (from Jane) will spend $$90 \%$$ of it, or $$\$ 0.81$$. This process of spending continues and results in an infinite geometric series as follows: $$1,0.90,0.90^{2}, 0.90^{3}, 0.90^{4}, \ldots$$

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Key Concepts

Multiplier Effect

The multiplier effect in economics describes how an initial change in spending leads to a larger overall change in economic activity due to the process of repeated spending. It illustrates the cumulative impact of expenditure throughout the economy as each round of spending generates further income and spending.

Convergence of an Infinite Series

Convergence of an infinite series occurs when the sum of an infinite number of terms approaches a finite limit. This is crucial when applying infinite series to economic phenomena like the multiplier effect, ensuring the model results in a realistic, bounded outcome.

Marginal Propensity to Consume

This concept refers to the proportion of an additional unit of income that a consumer spends on goods and services rather than saving. It is a central idea in macroeconomics, influencing models of consumer behavior and the overall effect of income changes on an economy.

Infinite Geometric Series

An infinite geometric series is a series of numbers in which each term after the first is found by multiplying the previous term by a constant ratio. In economic models, such series can be used to represent processes where effects diminish over time, such as successive rounds of spending.

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