The simple spending multiplier is a concept in economics that represents the ratio of the change in national income to the initial change in spending that brought it about. It reflects how additional spending leads to further increases in income and consumption throughout the economy.
The formula for the spending multiplier (k) is given by:
\[ k = \frac{1}{1 - MPC} \]
Where MPC is the marginal propensity to consume. The marginal propensity to consume is the fraction of any additional income that a household will spend on consumption rather than saving.
In your example, the marginal propensity to consume (MPC) is 0.8. Plugging this value into the formula for the spending multiplier, we get:
\[ k = \frac{1}{1 - 0.8} \]
Calculating this:
\[ k = \frac{1}{0.2} = 5 \]
This means that for every dollar of initial spending, the total increase in income (or GDP) will be five dollars as the initial spending circulates through the economy. The first dollar spent leads to an increase in income, and because the MPC is 0.8, consumers spend 80 cents of each additional dollar they receive, leading to further rounds of income increase from that spending.
So, if the government or any entity spends $1 million, using this multiplier:
\[ \text{Total increase in income} = k \times \text{Initial spending} = 5 \times 1,000,000 = 5,000,000 \]
Thus, an initial spending of $1 million will ultimately result in a total increase in income of $5 million in the economy.