So when it is said that GDP equals consumption plus investment, government expenditures and net exports (NX, which will be ignored.) The right side must always equal the left side. Let's put it into equation form and figure out how we know savings equals investment.
Given:
Y= GDP
C= Consumption
G= Government Expenditures
I= Investment
NX= Net Exports, which we ignore because we are proposing a closed economy.
S= Savings
t= taxes
The equation from above is: Y=C+G+I
We can re write this to state: Y-C-G=I
So If we take GDP and subtract out consumption and government consumption we are left with Savings. Y-C-G=S and therefore S=I
We can then rework Y-C-G=S to include taxes, t. S= (Y-t-C) + (t-G). You can see that the t, taxes, cancel each other out. In this manner we can see that Private Savings equals (Y-t-C) and Public Savings equals (t-G). Or in ingles, private savings is equal to the remaining GDP after taxes and Consumption. The tax monies transfer to the government who then spend, G. If t is greater than G than there is a surplus and if not there is a deficit. When we net public and private savings, what is remaining is investment.
Thus, from earlier we can see that the financial system ensures that S=I by moving the money from people who can save it to people who can invest it.
It is important not to think of savings and investment as interchangeable words, they are not in economics. You do not invest when you buy a bond, you are saving. An entity invest when it purchases capital, such as, buildings or machinery.
Supply and Demand for Funds
The familiar supply and demand chart. This shows that as the real interest rate falls more funds are demanded. That is, business and consumers can undertake projects that will earn them more than the rate of interest charged for utilizing the funds. Conversely, less firms will loan at lower interest rates because they will not make enough return to compensate them for given their funds to risky clients. The balance is struck in this example at 1200 and a real interest rate of 5.5%. This is because the "invisible hand" will correct any meandering. Let's imagine that the real interest rate was higher than 5.5%, say 7%. What would happen? Well, more people would think that 7% was a good deal, thus they would increase the supply of savings to be invested. This would push down interest rates because of the additional supply. The market will work back to its equilibrium.
Let's examine the current situation. The financial crisis of 2007 and 2008 has now caused people to put more towards savings. The savings rate is up to 5.2% from 4% in the first quarter. This means that there has been an increase in funds that can be loaned.
In our example, we can see that the supply shifts parallel to the right. This means there is now a lower "real*" rate of interest than in the previous quarter, as the funds have moved from 1,200 to about 1,350. So the current financial crisis has encouraged households and businesses to save rather than consuming the money.
What could cause the demand curve to shift? Any encouragement of investment, say a tax credit for buying an automobile. This would cause the demand curve to parallel shift to the right as more entities used the tax credit plus a loan to purchase a new automobile.
*Real versus nominal: nominal is the quoted interest rate you see on Bloomberg, or the Wall Street Journal. The "real" rate of interest is adjusted for inflation.
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