Determination of National Income: formula sheet

Key formulas

Two sector equilibrium

Y = C + I, and S = I

Saving equals investment at equilibrium (planned values).

Three sector equilibrium

S + T = I + G

Leakages S and T equal injections I and G.

Four sector equilibrium

S + T + M = I + G + X

Leakages on the left, injections on the right.

Aggregate expenditure (four sector)

Y = C + I + G + (X − M)

(X − M) is net exports.

Leakages and injections list

Leakages: S, T, M. Injections: I, G, X

Memory aid: leakages are STM, injections are IGX.

GNP at market price

GNP(MP) = GDP(MP) + NFIA

NFIA = income earned from abroad − income paid to foreigners. It can be negative.

Net aggregates

NDP(MP) = GDP(MP) − Depreciation; NNP(MP) = GNP(MP) − Depreciation

Depreciation is also called consumption of fixed capital.

Market price to factor cost

FC = MP − Net Indirect Taxes

Net indirect taxes = indirect taxes − subsidies. Apply this to any aggregate.

National Income

National Income = NNP(FC) = NNP(MP) − NIT

Equivalent: GNP(MP) − Depreciation − NIT.

Domestic vs national

NNP(FC) = NDP(FC) + NFIA

Add NFIA to move from domestic to national.

Personal income

Personal Income = National Income − Undistributed profits − Corporate tax − Social security contributions + Transfer payments

Transfer payments include pensions and unemployment allowances.

Disposable income

Disposable Income = Personal Income − Personal direct taxes

Disposable income = Consumption + Saving.

Value added

Value added = Value of output − Intermediate consumption

Value of output = sales + change in stock. Add up value added of all units to get GDP at market price.

Gross vs net value added

Net value added = Gross value added − Depreciation (consumption of fixed capital)

Net value added at market price minus net indirect taxes gives net value added at factor cost.

Product method

GDP at MP = Σ Gross value added of all sectors

Sectors: primary, secondary, tertiary.

Income method

NDP at FC = Compensation of employees + Operating surplus + Mixed income of self-employed

Operating surplus = rent + interest + profit. Add net factor income from abroad to get NNP at FC (national income).

Expenditure method

GDP at MP = C + I + G + (X − M)

C is private final consumption, I is gross domestic capital formation, G is government final consumption, X − M is net exports.

Market price to factor cost

GDP at FC = GDP at MP − Net indirect taxes, where Net indirect taxes = Indirect taxes − Subsidies

Subsidies lower market price relative to factor cost, so subtract subsidies from indirect taxes first to get net indirect taxes.

Gross to net

NDP = GDP − Depreciation; NNP = GNP − Depreciation

Net means after depreciation.

Domestic to national

GNP = GDP + Net factor income from abroad (NFIA)

NFIA = factor income received from abroad − factor income paid abroad.

GDP deflator

GDP deflator = (Nominal GDP ÷ Real GDP) × 100

Base year value is 100. Nominal GDP uses current prices, real GDP uses base-year prices.

Real GDP

Real GDP = (Nominal GDP ÷ GDP deflator) × 100

Rearranged form of the deflator. Use it to strip out inflation.

Nominal GDP

Nominal GDP = (Real GDP × GDP deflator) ÷ 100

Use when real GDP and the deflator are given.

Inflation from deflator

Inflation rate (%) = [(Deflator this year − Deflator last year) ÷ Deflator last year] × 100

Divide by last year's deflator, not this year's.

Real growth rate

Growth (%) = [(Real GDP this year − Real GDP last year) ÷ Real GDP last year] × 100

Always use real GDP to measure growth.

Per capita income

Per capita income = National income ÷ Population

Real per capita income uses real national income.

Consumption function

C = a + bY

a = autonomous consumption, b = MPC, Y = income.

Saving function

S = Y − C = −a + (1 − b)Y

Slope of the saving function is MPS.

Average propensity to consume

APC = C ÷ Y

Measured at one income level.

Marginal propensity to consume

MPC = ΔC ÷ ΔY

For C = a + bY, MPC = b.

Average propensity to save

APS = S ÷ Y

APC + APS = 1.

Marginal propensity to save

MPS = ΔS ÷ ΔY

MPC + MPS = 1.

Break-even income

Y = C, so Y = a ÷ (1 − b)

At this income saving is zero and APC = 1.

Investment

I = ΔK (addition to capital stock)

Investment rises when the interest rate falls or the marginal efficiency of capital rises.

Aggregate demand (two sector)

AD = C + I

Consumption plus planned investment. No government or foreign trade.

Aggregate supply

AS = Y = C + S

All income is either consumed or saved.

Consumption function

C = a + bY

a = autonomous consumption, b = MPC (marginal propensity to consume), 0 < b < 1.

Saving function

S = Y − C = −a + (1 − b)Y

1 − b is MPS. Saving is negative when Y is low enough.

Equilibrium condition (AD-AS)

Y = C + I

Planned AD equals output.

Equilibrium condition (S-I)

S = I

Planned saving equals planned investment.

Equilibrium income

Y = (a + I) ÷ (1 − b)

Valid when I is autonomous. Gives the same answer from both approaches.

Break-even income

Y = a ÷ (1 − b)

Income at which C = Y and S = 0.

Investment multiplier (two sector)

k = ΔY ÷ ΔI = 1 ÷ (1 − MPC) = 1 ÷ MPS

Valid when saving is the only leakage. MPC + MPS = 1.

Equilibrium income (two sector)

C = a + bY, so Y = (a + I) ÷ (1 − b)

a is autonomous consumption, b is MPC.

Equilibrium income with lump-sum tax

C = a + b(Y − T), so Y = (a − bT + I + G) ÷ (1 − b)

Consumption depends on disposable income Y − T.

Government expenditure multiplier

ΔY ÷ ΔG = 1 ÷ (1 − b)

For lump-sum taxes. Same size as the investment multiplier.

Tax multiplier

ΔY ÷ ΔT = −b ÷ (1 − b)

Negative: a tax rise lowers income. Smaller in size than the G multiplier.

Balanced budget multiplier

(1 ÷ (1 − b)) + (−b ÷ (1 − b)) = 1

Equal rise in G and T raises income by the same amount.

Multiplier with proportional tax

k = 1 ÷ (1 − b(1 − t))

t is the income tax rate.

Multiplier with tax and imports

k = 1 ÷ (1 − b(1 − t) + m)

m is the marginal propensity to import. Denominator equals total leakage rate.

Four-sector equilibrium

Y = C + I + G + X − M

Exports X are an injection, imports M a leakage.

Quick revision

• Circular flow: income flows from firms to households as factor payments, and back as spending on output.
• Leakages are saving, taxes and imports; injections are investment, government spending and exports.
• GNP = GDP + net factor income from abroad.
• NNP = GNP − depreciation (consumption of fixed capital).
• Factor cost = market price − indirect taxes + subsidies.
• National Income = NNP at market price − indirect taxes + subsidies = NNP at factor cost.
• Product, income and expenditure methods should give the same national income in principle.
• Transfer payments and sales of second-hand goods are not counted in national income.
• Real GDP = Nominal GDP ÷ Price index × 100.
• MPC + MPS = 1, and APC + APS = 1.
• Equilibrium in a simple two-sector model: Y = C + I, or equivalently S = I.
• Investment multiplier k = 1 ÷ (1 − MPC) = 1 ÷ MPS; a higher MPC gives a larger multiplier.
• Government expenditure multiplier = 1 ÷ (1 − MPC); tax multiplier (lump-sum tax) = −MPC ÷ (1 − MPC); with a proportional tax rate t, k = 1 ÷ (1 − MPC(1 − t)).
• Change in income = k × change in autonomous investment.

Common mistakes

• Treating investment as a leakage because money is being spent out of firms. Fix: Investment adds to spending on output, so it is an injection. Remember IGX.
• Treating all saving as a loss that leaves the economy permanently. Fix: Saving is a leakage from the consumption flow, but it can return as investment through financial markets. Equilibrium needs S to equal I.
• Subtracting NFIA when going from GDP to GNP, or adding it when NFIA is negative. Fix: Remember GNP = GDP + NFIA. If the question gives a negative NFIA, the result falls. If it gives income paid abroad and income earned abroad separately, compute earned − paid first.
• Adding subsidies and subtracting only taxes, or the reverse, when converting MP to FC. Fix: Use FC = MP − (indirect taxes − subsidies). Taxes raise MP above FC. Subsidies pull MP below FC.
• Counting the value of intermediate goods along with the final goods. Fix: Count either only final goods or only value added. Ask: is this used up in producing something else this year?
• Including transfer payments such as pensions, scholarships and unemployment allowances in national income. Fix: Include only payments for current production of goods and services. Transfers involve no production, so exclude them.
• Using nominal GDP to claim economic growth. Fix: Growth means more output. Use real GDP for growth. Nominal GDP also moves with prices.
• Writing the deflator as Real ÷ Nominal. Fix: Remember the deflator is above 100 when prices rise, so nominal (the larger figure) goes on top.
• Treating APC and MPC as the same thing. Fix: APC uses total C and total Y. MPC uses only the changes ΔC and ΔY.
• Using total values to find MPC. Fix: Always subtract the two rows first, then divide ΔC by ΔY.

Exam tips

• Learn the lists STM (leakages) and IGX (injections). Many MCQs only test this.
• Know which sectors each model has. Questions often ask what is missing in a two sector economy.
• In numerical questions, write the equilibrium equation first. It prevents sign errors.
• Watch for words like 'closed economy' (no foreign sector) and 'open economy' (has exports and imports).
• Read all four options. Some use the term withdrawals for leakages, so treat them as the same.
• Read the target aggregate in the last line first. Then pick only the switches you need.
• Watch the words 'domestic', 'national', 'gross', 'net', 'market price' and 'factor cost'. Examiners change one word to create a trap option.
• Expect distractor data such as direct taxes in an NNP question. Ignore anything the chain does not need.