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In macroeconomics, the short-run level of national production (Y) is determined by total aggregate demand for goods and services (Z). When demand rises, firms increase production and hire more workers; when demand falls, production cuts follow.

In a simple closed economy—an economy that does not trade with the rest of the world—total demand comes from three main economic actors:

1. Consumption (C): Total spending by households on consumer goods and services (e.g., food, entertainment, cars).

2. Investment (I): Spending by businesses on new capital equipment, factories, and residential housing. For now, we treat investment as exogenous (given from outside the model, denoted as fixed I).

3. Government Spending (G): Purchases of goods and services by central and local governments (e.g., healthcare, infrastructure, public salaries).

Putting these three components together gives our aggregate demand equation:

Z = C + I + G

To understand what drives changes in aggregate demand, we need to look closer at what determines household consumption.

Household consumption depends primarily on disposable income (Yd), which is total national income (Y) minus taxes paid to the government (T):

Yd = Y - T

We represent household behavior using a linear consumption function:

C = c0 + c1 × (Y - T)

This linear relationship contains two crucial parameters:

• Autonomous Consumption (c0): The level of consumption when disposable income is zero. It represents basic necessities (food, shelter) that people must buy regardless of current income, funded by drawing down past savings or taking out loans. If consumer confidence rises, c0 increases.
• Marginal Propensity to Consume (c1): The proportion of an extra dollar of disposable income that households spend on consumption. The value of c1 lies between 0 and 1 (0 < c1 < 1). For example, if c1 = 0.6, households spend 60 cents of every additional dollar of disposable income and save the remaining 40 cents.

Numerical Example:

Suppose autonomous consumption c0 = 100, marginal propensity to consume c1 = 0.6, total income Y = 1000, and taxes T = 200.

Disposable income Yd = 1000 - 200 = 800.

Consumption C = 100 + 0.6 × 800 = 100 + 480 = 580.

The goods market is in equilibrium when production (Y) equals total aggregate demand (Z):

Equilibrium Condition: Y = Z

We can find equilibrium national output algebraically by substituting our consumption function into the demand equation:

1. Start with the equilibrium condition:

Y = C + I + G

2. Substitute the consumption function C = c0 + c1(Y - T):

Y = c0 + c1(Y - T) + I + G

3. Expand the parentheses:

Y = c0 + c1 × Y - c1 × T + I + G

4. Collect all income terms (Y) on the left side:

Y - c1 × Y = c0 + I + G - c1 × T

5. Factor out Y on the left side:

(1 - c1) × Y = c0 + I + G - c1 × T

6. Divide both sides by (1 - c1):

Y* = [1 / (1 - c1)] × [c0 + I + G - c1 × T]

This final equation reveals two key macroeconomic components:

• Autonomous Demand [c0 + I + G - c1 × T]: The part of demand that does not depend on current output level Y.
• The Multiplier [1 / (1 - c1)]: A factor greater than 1 that scales up autonomous spending to determine equilibrium output Y*.

Why does a 10 billion increase in government spending (G) lead to a larger than10 billion increase in total output? This phenomenon is called the multiplier effect.

How the Multiplier Process Works Step-by-Step

Suppose c1 = 0.6, so the multiplier is 1 / (1 - 0.6) = 1 / 0.4 = 2.5. Let government spending increase by $10 billion:

• Round 1: Government buys 10B of goods. Production rises by10B, generating $10B of new income for workers and firm owners.
• Round 2: Recipients of this 10B income spend 60% (c1 = 0.6) on consumption, creating6B in new demand. Production rises by another $6B.
• Round 3: Recipients of the 6B spend 60% of it, creating3.6B in new demand...

The total increase in output is the sum of an infinite geometric series:

ΔY = ΔG × (1 + c1 + c1² + c1³ + ...) = ΔG × [1 / (1 - c1)]

ΔY = 10B × 2.5 =25 billion!

Adjustment Dynamics

In the real world, this adjustment does not happen overnight. When aggregate demand rises unexpectedly, firms first meet demand by selling out of existing inventories. As inventory levels drop, firms respond by increasing production and hiring workers over successive quarters until the economy settles at its new equilibrium Y*.