STEP-BY-STEP ANSWER:
Step 1: Define national savings, which comprises private savings and the government’s budget surplus (or accounts for a deficit).
Step 2: In a closed economy, recognize that personal and public sector savings must exactly equal domestic investment spending.
Step 3: In an open economy, understand that any imbalance between savings and domestic investment is adjusted by foreign capital inflows or outflows.
Step 4: Note that this identity underpins the entire mechanism in which capital is mobilized and allocated for growth.
Final Answer: The savings–investment spending identity establishes that total savings, whether generated solely within the economy or supplemented by foreign funds, is equal to the total investment, ensuring that available capital is fully utilized.