Q.Suppose $C = 40 + 0.8\,Y_D$, $T = 50$, $I = 60$, $G = 40$, $X = 90$, $M = 50 + 0.05\,Y$.

The Keynesian Cross: From Pocket Money to National Income

Imagine you and your friends decide to pool money for a party. You each contribute ₹100. The total pool is ₹500. Now, you spend that ₹500 on decorations, snacks, and music. The shopkeepers who sell you these things earn ₹500. They, in turn, spend some of that money on their own needs — maybe buying groceries or paying rent. That spending becomes someone else's income. A chain reaction begins.

This simple idea — that one person's spending becomes another person's income — is the heart of the Keynesian Cross. It's a way of understanding how the total income of a whole country is determined by how much people, businesses, and the government decide to spend.

The Core Idea: Spending Creates Income

The Keynesian Cross is a diagram that shows the relationship between total planned spending (what everyone intends to buy) and total output or income (what the economy produces). The central insight is this: the level of national income is not fixed. It adjusts until total planned spending equals total output.

Why? Because if people plan to spend more than what is currently being produced, shops run out of stock. Businesses see this and produce more, hiring more workers, which increases income. The opposite happens if spending is too low — unsold goods pile up, production is cut, and income falls.

The equilibrium — the resting point of the economy — is where these two forces balance.

The Two Lines That Tell the Story

The diagram has two lines on a graph. The horizontal axis measures national income or output ($Y$). The vertical axis measures aggregate demand — total planned spending ($AD$).

Line 1: The 45-degree line. This is a straight line at 45 degrees from the origin. Every point on this line has the property that the value on the vertical axis equals the value on the horizontal axis. In other words, it represents all points where output equals spending. It's the "what goes around comes around" line — if the economy lands on this line, everything produced is exactly bought.

Line 2: The Aggregate Demand line. This line shows total planned spending at each level of income. It slopes upward because as income rises, people spend more (on consumption). But it is flatter than the 45-degree line because not every extra rupee of income is spent — some is saved.

The equilibrium is where these two lines cross. At that single point, and only at that point, does total planned spending exactly equal total output. The economy has no reason to expand or contract.

The Precise Formula: What the NCERT Says

The NCERT gives a clear, formal statement of this equilibrium. Let's break it down.

This is the national income identity for a three-sector economy (households, firms, government). It says that total output ($Y$) must equal total spending on that output: consumption plus investment plus government purchases.

But the Keynesian cross adds a crucial twist. The $C$, $I$, and $G$ on the right-hand side are planned expenditures. The $Y$ on the left is actual output. Equilibrium occurs only when planned spending equals actual output.

The NCERT then introduces the consumption function, which shows how consumption depends on income:

Substituting this into the equilibrium condition gives:

Rearranging:

This $Y^*$ is the equilibrium level of national income. It is the exact point where the two lines cross on the Keynesian cross diagram.

Why the Denominator Matters: The Multiplier

The denominator $(1 - b)$ is the marginal propensity to save (MPS). If $b = 0.8$ (people spend 80% of extra income), then $1 - b = 0.2$. The equilibrium income becomes:

A small increase in autonomous spending (say, government builds a road worth ₹100 crore) leads to a five times larger increase in national income (₹500 crore). This is the investment multiplier:

The NCERT states this clearly: the multiplier tells you how many times the initial spending gets multiplied as it circulates through the economy. …