In the IS curve, interest rates are represented as a function of Gross Domestic Product (GDP). The initials I.S., in full, means the investment and saving equilibrium. It represents the locus points of all equilibriums; a point where total spending is equal to the total output of the economy (GDP or Y). Total spending may include the sum of government purchases, consumer spending, net imports, and private investments. The IS curve represents the equilibrium point where total saving equals the sum of all investments (private). Total savings are the sum of government savings from budgets, consumer saving, and savings from foreign trade. Real GDP (Y) is calculated based on the interest rates for each type of savings.
In an open economy, the interest rates will influence the level of investment. Generally, a decline in interest rates increases investor confidence. In this regard, income and a given interest rate are at the equilibrium level, when the consumer savings (from the income) is equal to investment. Thus, a high-income level would lead to a high consumer saving at a particular interest rate. Also, as the level of fixed investments increases, real GDP also increases giving the IS curve a negative slope. In general, the curve represents a point of causation, where falling interest rates lead to high planned fixed investment, which in turn leads to an increase in national output (GDP).
On the other hand, the IS curve in a closed economy is expressed as: Y = C (Y-T) + I (r) + G, where C (Y-T) is the total consumer spending (a function of income, Y, less taxes, T); I (r) represent planned investments (I) at a given interest rate (r); G is the total spending by the government; and Y is the total income of an economy. From this IS equation, government spending (G) and taxes (T) are exogenous factors. In an open economy, net exports (exports-imports) have to be included in the equation.