Posted on March 4, 2008 by Ben Connard
Slowing consumer spending has received much press lately as economists fear a decline will send our economy into a recession. Consumer spending accounts for two thirds of GDP. Business investment, government spending and net exports make up the last third.
When consumers don’t spend, businesses stop selling products, resulting in lay-offs and further slowing consumer spending. A vicious downward cycle can result. This cycle motivated the government’s $168 billion stimulus package put through last month.
A simple mathematical formula, based on the limit of sequences, can be used to explain why consumer spending is so important to our economy, and why the government wants you to spend your rebate checks.
For every $1 I earn, I hypothetically save 20% (or $0.20) and spend 80% (or $0.80). The $0.80 I spend is part of our consumer spending total. But the $0.80 also accounts for earnings for someone else. And let’s assume they also save 20% ($0.16) and spend 80% ($0.64). This $0.64 is also earnings for a third person, who then spends and saves at the same ratio.
Before you know it, we have a sequence of numbers: $0.80, $0.64, $0.51, $0.41… and so on. The aggregate sum of this infinite sequence approaches $4. In fact, any infinite sequence of numbers summed in a similar fashion where the “spend” percent is less than 100% will approach a finite number. The generic formula for finding the sum is: r/(1-r) where r is your ratio (80% in this case).
If we assume that all consumers spend less than 100% of their earnings, which ideally is the case, we can see how consumer spending becomes such a big portion of the economy. Every dollar spent feeds many more dollars into the economy.
This is part of the power behind the $168 billion stimulus package—in the example above the $168 billion could feed $672 billion ($168 billion times 4) into the economy.
However, if consumers spend a smaller portion of their rebate checks, the effect of the stimulus will be much less. When “r” is 50% the sum is 1 and when “r” is 20% the sum is 0.25. In other words, at 50% spending the stimulus package feeds only the original $168 billion into the economy. At 20% spending the stimulus package contribution falls to $42 billion.