## 11/12/11

### Why savings equals investment (S=I) and the financial sector notes

The Financial System:

The financial system is the system of financial markets and intermediaries through which households supply funds/money and firms demand it.  Financial markets are markets where stocks and bonds (also known as securities) are traded.  Financial intermediaries are companies including banks, insurance companies, mutual funds, and pension funds that borrow money from the savers in the economy and lend the money to borrowers.

Why Savings equals Investment:

Using the GDP equation to explain saving and investing:

Begin with our GDP equation for an open economy:

Y = C + I + G + NX

To simplify this idea, let’s look at a closed economy, where there are no imports or exports.  This means that NX will equal 0 and will therefore drop out.  This leaves us with:

Y = C + I + G

We can rearrange this equation to solve for investment (I) as a function of the other variables in the economy:

I = Y – C – G

This equation tells us that investment in the economy will be equal to the total amount produced (GDP = Y) minus consumption spending, and government purchases.

Now we can create a savings for the economy equation.  The total amount of private savings (savings by the private sector meaning households and firms) is going to be equal to the amount produced (Y) plus transfer payments from the government (we will call this TR, and include things like unemployment, social security and welfare) minus the amount spend on consumption (C) and taxes (T).

S(private) = Y + TR – C – T

Hopefully this makes sense, the amount you save (S) will be whatever is left over (starting from initial money of Y and TR) after you account for spending and expenses (C and T).

Now we need to consider public savings, which is how much the government saves.  Public spending depends on the amount of taxes they receive (T), the amount they spend in purchases (G), and the amount they transfer to the population (TR).  The public savings function will be:

S(public) = T – G – TR

We can find the total amount of savings (S) occurring in the economy by adding public savings to private savings.

S(public) + S(private) = S

T – G – TR + Y + TR – C – T =S

Note that T and TR cancel out.  This leaves us with savings (S) being equal to GDP (Y), government purchases (G), and consumption (C):

S = Y – G – C

If we plug in the GDP equation for Y, or substitute C + I + G for Y we get:

S = C + I + G – G – C

Note that C and G will cancel out leaving us with:

S = I

This shows that the total amount of savings occurring in the economy is equal to the amount being invested.  Remember that investment leads to the accumulation of capital which leads to increased labor productivity which leads to economic growth (which is a good thing).  So having high amounts of savings is good for economic growth.

Note that it is possible to have negative amounts of saving or dissaving.  For example, if T is less than G + TR then public saving will be negative.  Also, is C + T is greater than Y + TR then we will also have negative private saving, but this is very rare.

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