Principles of Macroeconomics / Unit 9 MAC 0832 review, 2 to 3 minutes
Why Closing a Gap Takes Less Than the Gap
The idea
The result that a 250 billion gap closes with 100 billion of spending is the point of the whole model, and it is worth seeing why it is not a trick. The extra spending does not stop when it is received. The firms that receive it pay workers and suppliers, whose incomes rise, and they spend a share of that on other firms, whose workers and suppliers then spend again. Each round is smaller than the one before, because at every round some of the money leaks out of the flow of spending on domestic output. Saving takes a share, taxes take a share, imports take a share. What is left circulates. Add the rounds and they converge on a total larger than the injection, and the ratio of the total to the injection is the multiplier. So the policy needed is the gap divided by that ratio, not the gap itself.
In practice
Worked example: an economy with a slope of 0.6 receives 100 billion of new government purchases. The first round is the 100 itself. The second is 0.6 of that, or 60. The third is 0.6 of 60, or 36, then 21.6, then about 13, then about 8, then about 5. After ten rounds the additions have fallen under two billion, and after twenty they are a rounding error. The rounds sum to 250. The same 250 comes out of the formula in one step, one divided by one minus 0.6. The round-by-round story and the formula are the same fact, and running the rounds once is worth doing, because it is what makes the formula stop looking arbitrary.
Where people slip
Three cautions. The multiplier works downward with equal force, so a collapse in business confidence or a slowdown in a trading partner is magnified the same way, which is part of how a recession deepens. The size of the multiplier is a tradeoff rather than a target: a high multiplier makes policy powerful but magnifies every shock, so the economy is more volatile, while a low multiplier gives a steadier economy and weaker policy leverage, and no setting delivers both. And every number here assumes the price level holds still, which is the assumption the next two entries examine and eventually withdraw.
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