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National Savings (S) refers to the total amount of savings in a country. It consists of two parts: private savings and public savings. Private savings represent the savings made by households and firms, while public savings represent the savings made by the government. National Savings can be represented as: National Savings (S) = Private Savings + Public Savings Private savings is the difference between disposable income (Income after taxes and transfers) and consumption: Private Savings = Y - T - C where Y is the total income, T is taxes, and C is consumption. Public savings is the difference between tax revenues and government spending: Public Savings = T - G where G is the government spending.

National Investment (I) refers to the total amount of investments made in a country. Investments here include capital formation, like the investment in infrastructure, businesses, and residential buildings.

In a closed economy, where there is no international trade, total savings and total investments are equal. There is a direct relationship between national savings and investments, and this relationship is referred to as the national savings and investment identity. The equation for a closed economy can be expressed as: National Savings (S) = National Investment (I) In an open economy, where there is international trade, we need to account for net exports (NX). Net exports are calculated as: Net Exports (NX) = Exports (X) - Imports (M) The equation for an open economy can be expressed as: National Savings (S) = National Investment (I) + Net Exports (NX) In conclusion, the two main sides of the national savings and investment identity are national savings (private savings and public savings) and national investment. These two sides balance each other in an open or closed economy, reflecting the relationship between a country's total savings and its total investments.