7.2 Savings and Investment

If you recall, investment, in the GDP sense, includes business fixed expenditures, new residential construction, and changes in inventories. By and large, these types of expenditures require large amounts of money. But where does this money come from? To discover the answer, we need to set up a system of equations. From Chapter 4, we recall that the GDP identity is:

[latex]Y=C+I+G+NX[/latex]

To simplify, we are going to assume we have a closed economy. This occurs when we do not trade with other economies, leading to [latex]NX=0[/latex].

In a closed economy, our new GDP identity is:

[latex]Y=C+I+G[/latex]

But we are interested in investment, so let us re-arrange the equation by solving for investment ([latex]I[/latex]):

[latex]I=Y-C-G[/latex]

This tells us that investment will be an economy’s income minus consumption and government spending.

Now, let us consider savings. We can split savings into two components: private savings, which refers to savings by households, and public savings, which refers to savings by governments.

In the private sector, households receive income by providing their factors of production, like labour, to firms ([latex]Y[/latex]). They also receive money from the government, which we call transfer payments in Chapter 4 ([latex]TR[/latex]). But households also spend money. Money spent on goods and services is classified under consumption ([latex]C[/latex]). Additionally, households must also pay taxes to the government ([latex]T[/latex]). Therefore, the private savings function can be written as:

[latex]S_\textrm{private}=Y+TR-C-T[/latex]

But the government will also engage in saving. The government earns money through the collection of taxes but spends money on its purchases (the “G” in the GDP identity) and transfer payments. Therefore, the public savings function can be written as:

[latex]S_\textrm{public}=T-G-TR[/latex]

Putting the two equations together, we then get total national (or aggregate) savings:

[latex]\begin{align*}S&=S_\textrm{private}+S_\textrm{public}\\[2ex]&=(Y+TR-C-T)+(T-G-TR)\\[2ex]&=Y+TR-TR+T-T-C-G\\[2ex]&=Y-C-G\end{align*}[/latex]

But where have we seen this before? In the investment function from earlier. Therefore,

[latex]S=I[/latex]

This means that for a country with a closed economy, the total savings in an economy will be equal to the total value of investments. In other words, savings finances investment. This is called macroeconomic identity. This identity implies that the primary fund for business investment comes from the total savings generated in the economy by households and governments.