Suppose the government increase its spending by $100 million. And suppose we are talking about intermediate level macroeconomic class. Let the marginal propensity to spend be 0.5.
Now the total GDP should increase by 100/0.5=200 because the increased spending increases people's income and thus further increase the spending, so on and so forth. But wait, what if the marginal propensity to spend is 0! Then we have an infinite increase in GDP! OR if this sounds just wrong, let us consider where the unspent money get saved in banks. And banks will lend the money out which induce firm to invest more. So the investment will increase people's income, and hence the same effect as before. So in the end, we see that the increase in government spending will increase income by the same amount, and then increase spending again by the same amount (the saving also get invested, so it increases the GDP), and etc.
This is clearly not the case in the world we live in. What is the catch?