Q.Suppose the following information is given about a hypothetical economy : C = 100 + 0·75 Y (where, C = Consumption and Y = Income) ; I0 = 200 (I0 = Autonomous Investment). Calculate the following on the basis of the given information :

We are given the consumption function $C = 100 + 0.75Y$ and autonomous investment $I_0 = 200$. The economy is a two-sector model with no government or foreign sector, so Aggregate Demand is $AD = C + I$.

1. Equilibrium Level of Income Equilibrium requires $Y = AD$. Substituting:

   $Y = C + I_0 = (100 + 0.75Y) + 200$

   $Y = 300 + 0.75Y$

   $Y - 0.75Y = 300$

   $0.25Y = 300$

   $Y = \frac{300}{0.25} = 1200$

2. Aggregate Demand at Equilibrium Level of Income At equilibrium, $AD = Y = 1200$. We can verify: $C = 100 + 0.75(1200) = 100 + 900 = 1000$, so $AD = 1000 + 200 = 1200$. …

Let’s work through this step by step. The core idea is that in a simple two-sector economy (households and firms), equilibrium occurs when total planned spending — Aggregate Demand (AD) — equals total output (Y). No firm wants to produce more than it can sell, and no household wants to spend more than its income allows, so the economy settles at the point where these two forces balance.

We are given:

• Consumption function: $C = 100 + 0.75Y$
• Autonomous investment: $I_0 = 200$

The $0.75$ in the consumption function is the Marginal Propensity to Consume (MPC) — the fraction of each additional rupee of income that households spend on consumption. The $100$ is autonomous consumption, the spending that happens even when income is zero (financed by past savings or borrowing).

(a) Equilibrium Level of Income

At equilibrium, output $Y$ equals Aggregate Demand $C + I$. Substitute the given functions:

Simplify the right-hand side:

Now bring the term involving $Y$ to the left:

Divide both sides by $0.25$:

So the equilibrium level of income is ₹1,200.

(b) Aggregate Demand at Equilibrium Level of Income

Once we know equilibrium income, we can find Aggregate Demand by plugging $Y = 1200$ into the AD equation:

First compute consumption:

Then add investment:

Notice that at equilibrium, $AD = Y = 1200$. This is not a coincidence — it is exactly what the equilibrium condition guarantees. The economy produces exactly what is demanded, so there is no unplanned inventory accumulation or depletion.

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