Final answer:
The identity between national savings and investment holds only in a closed economy, where all economic activity is domestic and there is no international trade. In such economies, national savings must equal national investments as there are no external financial capital flows.
Step-by-step explanation:
Identity between National Savings and Investment
The identity between national savings and investment holds only in a closed economy. In this context, the terms savings and investment refer to national financial capital. The formula for this identity in a closed economy states: national savings equal national investment (S = I). Private saving plus government saving (which is taxes minus government spending), without factoring in international trade, equals the total national investment.
This identity holds in a closed economy because it does not engage in international trade, meaning there are no exports (X) or imports (M), and thus the savings within the country must be used to fund all investment.
Mixed economies, on the other hand, have both private sector and government involvement in economic decision-making, which includes international trade. Therefore, the national saving and investment identity may not hold in a mixed economy due to the influence of foreign investment and savings.
In an open economy, with international trade, the formula would be modified to include net exports (exports minus imports), and the identity might not balance if the country is engaging in borrowing from or lending to other countries.