Q.What is 'effective demand'? How will you derive the autonomous expenditure multiplier when price of final goods and the rate of interest are given?

Effective Demand and the Autonomous Expenditure Multiplier

Effective demand is the level of aggregate demand (total planned expenditure) at which aggregate demand equals aggregate supply in an economy. It represents the equilibrium output where firms have no incentive to change production because planned spending exactly matches what they produce. Keynes introduced this concept to explain how equilibrium output is determined by demand-side factors, not just supply capacity.

Deriving the Autonomous Expenditure Multiplier

When the price of final goods and the rate of interest are given (held constant), we work in a simple Keynesian model where consumption depends on income and investment is autonomous.

Start with the equilibrium condition:

where $Y$ is income, $C$ is consumption, and $I$ is autonomous investment. Consumption has the form $C = \bar{C} + cY$, with $\bar{C}$ as autonomous consumption and $c$ as the marginal propensity to consume (MPC).

Substituting:

Rearranging:

$Y = \frac{1}{1-c}(\bar{C} + I)$ …

Effective Demand: The Equilibrium Concept

Effective demand is not simply what people want to buy—it is the particular level of aggregate demand that actually gets realized in the economy when production decisions validate it. Think of it as the point where plans meet reality.

Firms produce output based on what they expect people will buy. If aggregate demand (consumption plus investment plus government spending) turns out to equal the value of output produced, firms have guessed right: inventories neither pile up nor run short, and there is no pressure to expand or contract production. This equilibrium level of output, where planned aggregate demand equals actual output, is what Keynes called effective demand. It is "effective" because it translates into actual employment and production, not merely wishful thinking.

The crucial insight: in the short run, with spare capacity and sticky prices, output adjusts to meet demand rather than the other way around. Effective demand therefore determines the level of national income and employment.

Deriving the Autonomous Expenditure Multiplier

When the price level and the interest rate are held constant (the short-run Keynesian assumption), we can derive the multiplier algebraically from the equilibrium condition.

Step 1: Write down aggregate demand

Aggregate demand $AD$ has two components: consumption $C$, which depends on income, and autonomous expenditure $\bar{A}$, which does not. Autonomous expenditure bundles together investment, government spending, and the part of consumption that does not vary with income (the intercept).

The consumption function is

where $\bar{C}$ is autonomous consumption, $c$ is the marginal propensity to consume ($0 < c < 1$), and $Y$ is national income. Aggregate demand is then

where $\bar{A} = \bar{C} + \bar{I} + \bar{G}$ is total autonomous expenditure.

Step 2: Impose the equilibrium condition

At equilibrium (effective demand), actual output equals planned spending:

Step 3: Solve for equilibrium income

Rearrange:

This tells us equilibrium income as a function of autonomous spending.

Step 4: Find the multiplier

The autonomous expenditure multiplier $k$ measures how much equilibrium income changes when autonomous expenditure changes by one unit. Differentiate (or take a small change):

so

Equivalently, since $c$ is the marginal propensity to consume and $s = 1 - c$ is the marginal propensity to save,

The Economic Intuition …