Effective demand refers to that level of aggregate demand where the aggregate demand for final goods equals the aggregate supply of final goods at a particular price level. Under conditions where the price of final goods and rate of interest are constant, and aggregate supply is perfectly elastic, aggregate output is determined solely by the level of aggregate demand. This is known as the effective demand principle.

To derive the autonomous expenditure multiplier, we must understand that an initial increment in autonomous expenditure leads to a larger increase in equilibrium output through the multiplier mechanism. When autonomous expenditure increases, it raises income, which in turn increases consumption expenditure based on the marginal propensity to consume (mpc).

The process works through successive rounds. If autonomous expenditure increases by ΔA, the total increase in equilibrium output equals ΔA + (mpc)ΔA + (mpc)²ΔA + ... This forms an infinite geometric series that sums to ΔY = ΔA/(1-mpc).

Thus, the multiplier (k) is derived as the ratio of total increment in equilibrium output to the initial increment in autonomous expenditure: k = 1/(1-mpc). For example, if mpc = 0.8, then multiplier = 1/(1-0.8) = 5, meaning an increase of 10 units in autonomous expenditure raises equilibrium output by 50 units.