A. Some Important Identities
1. Remember that GDP can be divided up into four components: consumption, investment, government purchases, and net exports.
2. We will assume that we are dealing with a closed economy (an economy that does not engage in international trade). This implies that GDP can now be divided into only three components:
3. To isolate investment, we can subtract C and G from both sides:
4. The left-hand side of this equation (Y – C – G) is the total income in the economy after paying for consumption and government purchases. This amount is called national saving.
5. Definition of National Saving (Saving): the total income in the economy that remains after paying for consumption and government purchases.
6. Substituting saving (S) into our identity gives us:
7. This equation tells us that saving equals investment.
8. Let’s go back to our definition of national saving once again:
9. We can add taxes (T) and subtract taxes (T):
10. The first part of this equation (Y – T – C) is called private saving; the second part (T – G) is called public saving.
a. Definition of Private Saving: the income that households have left after paying for taxes and consumption.
b. Definition of Public Saving: the tax revenue that the government has left after paying for its spending.