Determination of Income and Employment

How output is set by aggregate demand: the consumption function, MPC and MPS, equilibrium income, the multiplier, unplanned inventories and the paradox of thrift.

Key ideas

The consumption function C = C̄ + cY has autonomous consumption C̄ and the marginal propensity to consume c.
Extra income is either consumed or saved, so MPC + MPS = 1.
Ex ante means planned; ex post means actual. In a two-sector model aggregate demand is planned C + I.
Equilibrium output is where aggregate demand equals output; there planned saving equals planned investment.
If output exceeds AD, unsold stocks pile up and firms cut output; if output falls short, stocks run down and firms raise output.
A rise in autonomous spending raises income by a multiple, because each round of extra income is partly spent again.
Paradox of thrift: if everyone tries to save more, income falls and total saving does not rise. Equilibrium below full employment means deficient demand; above it, excess demand.

Remember

MPC and MPS	MPC = ΔC ÷ ΔY; MPS = ΔS ÷ ΔY = 1 − MPC
APC and APS	APC = C ÷ Y; APS = 1 − APC
Equilibrium income	Y = (C̄ + I) ÷ (1 − c)
Investment multiplier	k = 1 ÷ (1 − MPC) = 1 ÷ MPS
Change in income	ΔY = k × ΔI; investment needed = ΔY ÷ k
Saving at income Y	S = Y − (C̄ + cY)
Unplanned inventory change	output − AD, where AD = C̄ + I + c × output

Watch out

Using 1 ÷ MPC as the multiplier instead of 1 ÷ (1 − MPC).
Forgetting autonomous consumption C̄ when working out consumption or saving.
Saying inventories run down when output is above aggregate demand (they pile up).

Worked example

Suppose C = 150 + 0.75Y and I = 200 (₹ crore). Find equilibrium income, consumption and saving there.

Working: Y = (150 + 200) ÷ 0.25; C = 150 + 0.75 × 1,400

Answer: Y ₹1,400 crore; C ₹1,200 crore; S ₹200 crore (= I)