# How do government purchases crowd out the private sector?

I am curious about how government purchases crowd out the private sector (if it does). If we look at a graph of the composition of US GDP, it seems that government purchases and investment are somewhat negatively correlated. It's obvious during WWII that government purchases skyrocketed while investment shrank significantly.

I am wondering about the intuition behind why this happens. If I had to guess, it's because at a given snapshot in time, the capital and labor in the economy is limited, and if the government is spending more money to use capital goods and labor, then there are less capital goods to go around for the investment. Is that line of thinking correct?

Making the naïve and somewhat incorrect assumption that savings are fixed, every dollar that goes to government spending (e.g. defence, health, education, roads) is a dollar taken away from private investment. This is what is meant by crowding out.

A bit more precisely, we have in a closed economy the following identity: $$Y=C+I+G.$$

We define savings by $$S:=Y-C-G.$$

And hence, $$S=I.$$

So, making the naïve and somewhat incorrect assumption that $$S$$ is fixed, if $$G$$ rises by $$\1$$, then it must necessarily be that $$I$$ falls by $$\1$$.

The argument above is that sometimes given by opponents of increased government spending.

Supporters of increased government spending counter that the assumption that savings are fixed is naïve and somewhat incorrect. Savings are not fixed, they say. In particular, when $$G$$ rises by $$\1$$, $$Y$$ may also rise, so that $$I$$ need not mechanically fall by $$\1$$.

But even if this counterargument is correct, there will still probably be at least some crowding out. That is, when $$G$$ rises by $$\1$$, it is likely that $$I$$ falls by some amount less than $$\1$$.

• I think saving is defined as $S:=Y-C-G$, i.e. total national income minus total private and public expenditure. – Herr K. Jan 27 at 4:39
• @HerrK. You are of course right. Now corrected. – Kenny LJ Jan 27 at 4:46