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Identify the correct expression to calculate equilibrium level of income of an economy.

Solution

✅ Correct Option: 2

Option 1 -> This divides by MPC instead of MPS, which is incorrect for the multiplier formula.

Option 2 -> Uses the correct formula: Y = (C̄ + Ī)/MPS, where (1/MPS) is the spending multiplier.

Option 3 -> Incomplete formula that excludes autonomous investment (Ī).

Option 4 -> Incomplete formula that excludes autonomous consumption (C̄).


Hence, Option 2: (C̄ + Ī)/MPS -> At equilibrium, Y = C + I. With consumption function C = C̄ + cY, we get Y = C̄ + cY + Ī. Solving for Y: Y(1-c) = C̄ + Ī, so Y = (C̄ + Ī)/(1-c). Since MPS = 1 - MPC = 1 - c, the equilibrium income is Y = (C̄ + Ī)/MPS. The term (1/MPS) is the spending multiplier that shows how autonomous spending affects equilibrium income. -> correct

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