Q.In the above question, calculate the effect on output of a 10 per cent increase in transfers, and a 10 per cent increase in lump-sum taxes. Compare the effects of the two.

The question asks for the effect on output of a 10% increase in transfers and a 10% increase in lump-sum taxes, and a comparison of the two. This is a numerical question requiring the use of the government expenditure multiplier and the tax/transfer multiplier from the Keynesian cross model.

We start with the standard identity for aggregate demand in a closed economy with government:

$AD = C + I + G$

where consumption is $C = \bar{C} + c(Y - T + TR)$, with $c$ the marginal propensity to consume (MPC), $T$ lump-sum taxes, and $TR$ transfers. Investment $I$ and government spending $G$ are autonomous.

The equilibrium condition $Y = AD$ gives:

$Y = \bar{C} + c(Y - T + TR) + I + G$

Solving for $Y$:

$Y = \frac{1}{1-c} (\bar{C} + I + G - cT + cTR)$

The multiplier for a change in transfers is $\frac{\Delta Y}{\Delta TR} = \frac{c}{1-c}$, and for a change in lump-sum taxes it is $\frac{\Delta Y}{\Delta T} = -\frac{c}{1-c}$.

A 10% increase in transfers means $\Delta TR = 0.10 \times TR$. A 10% increase in lump-sum taxes means $\Delta T = 0.10 \times T$. The effect on output is:

$\Delta Y_{TR} = \frac{c}{1-c} \times 0.10 \times TR$

$\Delta Y_T = -\frac{c}{1-c} \times 0.10 \times T$ …

Let’s start with the core idea. In the simple Keynesian cross model (the one you study in NCERT Class XII Macroeconomics, Chapter 5), the equilibrium condition is:

where consumption depends on disposable income: $C = \bar{C} + MPC \times (Y - T + TR)$. Here, $T$ is lump-sum taxes and $TR$ is transfers. Investment $I$ and government spending $G$ are autonomous. The multiplier for any autonomous change in spending is $\frac{1}{1-MPC}$. But transfers and taxes don’t directly enter aggregate demand — they first change disposable income, which then changes consumption by the MPC.

Why the difference? A rupee of government spending directly adds to $G$ in the $C+I+G$ equation. A rupee of transfers (or a rupee cut in taxes) only increases disposable income by a rupee, and only $MPC$ of that gets spent on consumption. So the multiplier is smaller — it’s the MPC times the spending multiplier.

Now, the question asks: what happens if transfers increase by 10%, and separately if lump-sum taxes increase by 10%? We need the initial level of transfers ($\bar{TR}$) and taxes ($\bar{T}$) to compute the absolute change. The problem doesn’t give specific numbers for $\bar{TR}$ or $\bar{T}$, so we’ll express the answer in terms of those initial values.

Let the initial equilibrium be at $Y^*$. A 10% increase in transfers means $\Delta TR = 0.1 \times \bar{TR}$. The change in output is:

Similarly, a 10% increase in lump-sum taxes means $\Delta T = 0.1 \times \bar{T}$. The change in output is:

Applying this to the previous question. Question 6 specifies $C = 20 + 0.80\,Y$ (so $MPC = 0.80$) with transfers $\overline{TR} = 100$. A 10 per cent rise in transfers is $\Delta \overline{TR} = 0.1 \times 100 = 10$, and with $\frac{MPC}{1-MPC} = \frac{0.80}{0.20} = 4$ the effect on output is $\Delta Y = 4 \times 10 = 40$ — equilibrium income rises by 40. The "10 per cent increase in lump-sum taxes", however, cannot be pinned to a single number in the same setting: part (a) of Question 6 has no lump-sum tax at all ($\bar{T} = 0$), so 10 per cent of zero is zero and the comparison is genuinely undefined for that base case. A lump-sum tax appears only in part (c) of Question 6, where $\bar{T} = 30$; taking that as the reference, a 10 per cent increase is $\Delta \bar{T} = 3$ and the effect would be $\Delta Y = -4 \times 3 = -12$. We state this honestly rather than invent a tax base: since $\overline{TR} = 100$ is larger than $\bar{T} = 30$, the transfer change has the larger absolute effect on output. …