Equilibrium Level of Income — The Consumption-Investment (C+I) Approach

In a simple two-sector economy (households and firms only, no government or foreign trade), total planned expenditure (Aggregate Demand) consists of just consumption and investment: $AD=C+I$. National income is said to be in equilibrium when the total output produced (Aggregate Supply, which in this simple model equals income Y) exactly equals total planned expenditure:

Substituting the linear consumption function $C=a+bY$ and treating investment as autonomous (a fixed amount $I$, not varying with income):

Solving for the equilibrium level of income:

An equivalent, alternative derivation — the Saving-Investment (S=I) approach. Since $S=Y-C$, the equilibrium condition $Y=C+I$ can be rearranged as $Y-C=I$, i.e., $S=I$ — equilibrium income can equally be found as the level of income at which planned SAVING exactly equals planned INVESTMENT. Both approaches (the $C+I$ approach and the $S=I$ approach) are simply two algebraically equivalent ways of stating the SAME equilibrium condition, and MUST always yield the identical equilibrium income when applied to the same underlying consumption and investment data — solving via one method is therefore a valid way to CHECK a solution found via the other. …