Determination of Income and Employment — Notes

The model is short-run: prices are fixed, firms have spare capacity, and output is set by planned spending.

• Aggregate demand (AD): total planned (ex-ante) expenditure on final goods and services. Two-sector economy: AD = C + I; open economy with a government: AD = C + I + G + (X − M).
• Aggregate supply (AS): the value of output, equal to national income: AS = Y = C + S; shown by the 45° line.
• Ex-ante vs ex-post: planned versus actual values. Actual investment includes unplanned changes in inventories, so ex-post saving always equals ex-post investment.
• Autonomous investment: planned investment that does not change with income (a horizontal line).

Consumption function: C = c̄ + bY, where c̄ (autonomous consumption) > 0 and b = MPC.

• APC = C ÷ Y; MPC = ΔC ÷ ΔY, with 0 < MPC < 1.
• Saving function: S = Y − C = −c̄ + (1 − b)Y; APS = S ÷ Y; MPS = ΔS ÷ ΔY.
• APC + APS = 1 and MPC + MPS = 1, because income is either consumed or saved.
• Break-even point: C = Y and S = 0; for C = 100 + 0.75Y it is at Y = 100 ÷ 0.25 = 400.
• Below break-even, C > Y: APC > 1 and saving is negative (dissaving). APC falls as income rises; MPC is constant for a straight-line function. APC can exceed 1; MPC cannot (in the usual model).

Two equivalent conditions:

1. AD = AS (C + I = Y): AD cuts the 45° line at E.
2. Planned S = planned I: the saving curve cuts the investment line.

Formula: Y = (c̄ + I) ÷ (1 − MPC). Example: C = 100 + 0.75Y, I = 50 gives Y = 150 ÷ 0.25 = 600; at 600, S = −100 + 150 = 50 = I.

Adjustment: if AD > AS, stocks fall below plan and firms raise output; if AD < AS, stocks pile up and firms cut output. Prices do not move (fixed in the short run); quantities adjust.

Do not confuse the break-even income (C = Y, here 400) with equilibrium income (AD = Y, here 600).

K = ΔY ÷ ΔI = 1 ÷ (1 − MPC) = 1 ÷ MPS.

• Spending by one person is income for another; each round a fraction (the MPC) is re-spent and the rest is saved, so the rounds shrink and add up to K × ΔI.
• MPC 0.75 → K = 4; MPC 0.8 → K = 5; MPC 0.5 → K = 2.
• Range: K = 1 when MPC = 0; K grows without limit as MPC approaches 1. A higher MPC means a larger multiplier.
• Diagram: the AD line shifts up by ΔI; equilibrium income rises by K × ΔI (in the deck economy, 20 × 4 = 80, from 600 to 680).
• At the new equilibrium, the extra saving generated equals the extra investment.

• Full employment: all who are able and willing to work at the prevailing wage have work. Output is at its maximum with existing resources. Some voluntary and frictional unemployment remains.
• Involuntary unemployment: people willing to work at the prevailing wage cannot find work.
• Voluntary unemployment: people choose not to work at the prevailing wage.
• Keynesian point: in the short run, output is set by AD, so the equilibrium can lie below full-employment output (Y_F), with involuntary unemployment that does not disappear by itself.

Excess demand: AD > AS at full-employment output; the excess is the inflationary gap. Output and employment cannot rise, so prices rise.

Deficient demand: AD < AS at full-employment output; the shortfall is the deflationary gap. Stocks pile up, output and employment fall, involuntary unemployment appears, prices tend to fall.

Measuring: find AD at Y_F and compare with Y_F. For AD = 240 + 0.5Y: with Y_F = 360, AD = 420, inflationary gap 60; with Y_F = 600, AD = 540, deflationary gap 60, and extra spending of (600 − 480) ÷ 2 = 60 closes it.

Fiscal measures (budget): government spending, taxes, public borrowing. Against excess demand: cut spending, raise taxes, borrow more from the public; against deficient demand, the reverse.

Monetary measures (central bank; in India the RBI, whose policy repo rate is set by its Monetary Policy Committee): repo rate and bank rate, CRR, SLR, open market operations, margin requirements. Against excess demand: raise the rates and ratios, sell securities, raise margins; against deficient demand, the reverse.