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Questions › GATE › GATE 2023 › Q60
2 marksMacroeconomics › Keynesian cross and the multiplier › Government spending and tax multipliersModerateabout 2 min

GATE 2023 Question 60: Keynesian cross and the multiplier

Consider the Keynesian Cross Model with a linear consumption function and a zero tax, where the government purchase is Rs. 100 and the equilibrium income is Rs. 1300. If the government purchase is increased to Rs. 125, the equilibrium income increases to Rs. 1400. Using the given information, the marginal propensity to consume is ______ (round off to two decimal places).

Answer and worked solution

Answer: 0.71 to 0.79

ΔG=125−100=25,ΔY=1400−1300=100\Delta G = 125-100 = 25, \qquad \Delta Y = 1400-1300 = 100ΔG=125−100=25,ΔY=1400−1300=100

The government spending multiplier is:

Multiplier=ΔYΔG=10025=4\text{Multiplier} = \frac{\Delta Y}{\Delta G} = \frac{100}{25} = 4Multiplier=ΔGΔY​=25100​=4

Since the multiplier equals 11−MPC\dfrac{1}{1-MPC}1−MPC1​:

4=11−MPC⇒1−MPC=14=0.25⇒MPC=0.754 = \frac{1}{1-MPC} \quad\Rightarrow\quad 1-MPC = \frac{1}{4} = 0.25 \quad\Rightarrow\quad MPC = 0.754=1−MPC1​⇒1−MPC=41​=0.25⇒MPC=0.75

Therefore the marginal propensity to consume is 0.75, within the key's accepted range of 0.71 to 0.79.

The trap: 4.0

Students sometimes stop after computing the multiplier (4) and report that value directly, forgetting the question asks specifically for MPC, which requires one more algebraic step to invert 1/(1−MPC)=41/(1-MPC)=41/(1−MPC)=4 and solve for MPC itself.

Keynesian cross and the multiplier has come up 167 times in 7 exams since 2006.

What this question tests

This question is on Government spending and tax multipliers, part of Keynesian cross and the multiplier in Macroeconomics.

The effect on income of changes in government spending, lump-sum taxes, transfers and income taxes.

TestStop has 45 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q46With C = C₀ + b(Y - T), T = T₀ + tY, Y = C + I₀ + G₀, b = 0.75 and t = 0.1, an increase in G₀ by Rs. 20…
Take this paper as a timed mockMore on Government spending and tax multipliers

Question from the GATE 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.