The circular flow of income

The Multiplier Process

Definition of the Multiplier

The multiplier measures the number of times by which a change in national income is greater than the initial change in aggregate demand (AD).

When there is an increase in spending, one person’s expenditure becomes another person’s income. The recipient then spends part of this additional income, creating income for others.

→ An increase in investment → higher income for workers and suppliers → higher consumption expenditure → increased income for other firms and workers → further increases in consumption.

The process continues, but each successive increase becomes smaller because some additional income is saved, taxed or spent on imports.

Example:

A firm invests an additional ₹100 million in new machinery.

→ Suppliers receive ₹100 million in additional revenue.

→ Workers and suppliers earn additional income.

→ They spend part of this income on goods and services.

→ Other firms receive additional revenue and pay more wages.

→ National income increases by more than the original ₹100 million, assuming spare productive capacity and other multiplier conditions.

The Multiplier Formula

The basic formula is:

$$\boxed{k=\frac{\Delta Y}{\Delta AD}}$$k=ΔADΔY​​

Where:

• $k$k = multiplier
• $\Delta Y$ΔY = change in national income
• $\Delta AD$ΔAD = initial change in aggregate demand

Therefore:

$$\boxed{\Delta Y=k\times\Delta AD}$$ΔY=k×ΔAD​

Example:

An increase in investment of ₹50 million causes national income to rise by ₹200 million.

$$k=\frac{200}{50}=\boxed{4}$$k=50200​=4​

The multiplier is 4. Every ₹1 of initial additional spending results in a total increase of ₹4 in national income.

The Multiplier in a Closed Economy Without Government

A closed economy has no international trade. Without a government sector, there are no taxes or government expenditure.

The multiplier depends on the marginal propensity to consume (MPC) or the marginal propensity to save (MPS).

$$\boxed{k=\frac{1}{1-MPC}}$$k=1−MPC1​​

Since:

$$MPC+MPS=1$$MPC+MPS=1

The formula can also be written as:

$$\boxed{k=\frac{1}{MPS}}$$k=MPS1​​

Example:

If MPC = 0.8:

$$k=\frac{1}{1-0.8} =\frac{1}{0.2} =\boxed{5}$$k=1−0.81​=0.21​=5​

Alternatively, MPS = 1 − 0.8 = 0.2.

$$k=\frac{1}{0.2}=\boxed{5}$$k=0.21​=5​

If investment increases by ₹20 million:

$$\Delta Y=5\times ₹20\text{ million}$$ΔY=5×₹20 million

$$\boxed{\Delta Y=₹100\text{ million}}$$ΔY=₹100 million​

The Multiplier in an Open Economy Without Government

An open economy trades with other countries. Some additional income is spent on imports, which represents a leakage from the domestic circular flow of income.

If there is no government sector, the multiplier is:

$$\boxed{k=\frac{1}{MPS+MPM}}$$k=MPS+MPM1​​

Since $MPS=1-MPC$MPS=1−MPC, this can also be written as:

$$\boxed{k=\frac{1}{1-MPC+MPM}}$$k=1−MPC+MPM1​​

Where MPM is the marginal propensity to import.

Example:

Suppose:

• MPC = 0.7
• MPS = 0.3
• MPM = 0.1

$$k=\frac{1}{0.3+0.1} =\frac{1}{0.4} =\boxed{2.5}$$k=0.3+0.11​=0.41​=2.5​

If exports increase by ₹40 million:

$$\Delta Y=2.5\times ₹40\text{ million}$$ΔY=2.5×₹40 million

$$\boxed{\Delta Y=₹100\text{ million}}$$ΔY=₹100 million​

Imports reduce the multiplier because some additional expenditure benefits foreign producers rather than domestic producers.

The Multiplier in a Closed Economy With Government

In a closed economy with a government sector, taxes reduce the amount of additional income available for consumption.

If the tax rate is proportional and $MRT$MRT represents the marginal rate of tax:

$$\boxed{k=\frac{1}{MPS+MRT}}$$k=MPS+MRT1​​

This formula assumes there are no imports and that the marginal rate of tax applies to additional income.

Since $MPS=1-MPC$MPS=1−MPC:

$$\boxed{k=\frac{1}{1-MPC+MRT}}$$k=1−MPC+MRT1​​

Example:

Suppose:

• MPC = 0.75
• MPS = 0.25
• MRT = 0.20

$$k=\frac{1}{0.25+0.20} =\frac{1}{0.45} =\boxed{2.22}$$k=0.25+0.201​=0.451​=2.22​

If government spending increases by ₹45 million:

$$\Delta Y=2.22\times ₹45\text{ million}$$ΔY=2.22×₹45 million

$$\boxed{\Delta Y\approx ₹100\text{ million}}$$ΔY≈₹100 million​

The multiplier is smaller than it would be without taxation because part of additional income is paid to the government.

The Multiplier in an Open Economy With Government

When an economy has households, firms, government and international trade, additional income can leak out through saving, taxation and imports.

The multiplier is:

$$\boxed{k=\frac{1}{MPS+MRT+MPM}}$$k=MPS+MRT+MPM1​​

This formula assumes a proportional tax system and that the marginal rates remain constant.

Example:

Suppose:

• MPC = 0.7
• MPS = 0.3
• MRT = 0.2
• MPM = 0.1

$$k=\frac{1}{0.3+0.2+0.1} =\frac{1}{0.6} =\boxed{1.67}$$k=0.3+0.2+0.11​=0.61​=1.67​

If investment increases by ₹60 million:

$$\Delta Y=1.67\times ₹60\text{ million}$$ΔY=1.67×₹60 million

$$\boxed{\Delta Y\approx ₹100\text{ million}}$$ΔY≈₹100 million​

The multiplier is relatively small because saving, taxation and imports reduce the amount of additional income that is repeatedly spent within the domestic economy.

Summary of Multiplier Formulae

Economy	Multiplier formula
Closed, no government	$k=\frac{1}{MPS}$k=MPS1​
Open, no government	$k=\frac{1}{MPS+MPM}$k=MPS+MPM1​
Closed, with government	$k=\frac{1}{MPS+MRT}$k=MPS+MRT1​
Open, with government	$k=\frac{1}{MPS+MRT+MPM}$k=MPS+MRT+MPM1​

Important: These simplified formulae assume that the relevant marginal leakages are constant. Use the formula that matches the sectors included in the question.

Calculating Average and Marginal Propensities

Average Propensity to Consume (APC)

The average propensity to consume (APC) is the proportion of total income spent on consumption.

$$\boxed{APC=\frac{C}{Y}}$$APC=YC​​

Where:

• $C$C = total consumption expenditure
• $Y$Y = total income

Example:

Income = ₹50,000

Consumption expenditure = ₹40,000

$$APC=\frac{40,000}{50,000}=\boxed{0.8}$$APC=50,00040,000​=0.8​

This means 80% of income is spent on consumption.

Marginal Propensity to Consume (MPC)

The marginal propensity to consume (MPC) is the proportion of an additional unit of income spent on consumption.

$$\boxed{MPC=\frac{\Delta C}{\Delta Y}}$$MPC=ΔYΔC​​

Where $\Delta C$ΔC is the change in consumption and $\Delta Y$ΔY is the change in income.

Example:

Income increases from ₹50,000 to ₹60,000.

Consumption increases from ₹40,000 to ₹47,000.

$$MPC=\frac{47,000-40,000}{60,000-50,000}$$MPC=60,000−50,00047,000−40,000​

$$MPC=\frac{7,000}{10,000}=\boxed{0.7}$$MPC=10,0007,000​=0.7​

Of every additional ₹1 earned, ₹0.70 is spent on consumption.

Average Propensity to Save (APS)

The average propensity to save (APS) is the proportion of total income that is saved.

$$\boxed{APS=\frac{S}{Y}}$$APS=YS​​

Where $S$S = total saving.

If income is ₹50,000 and saving is ₹10,000:

$$APS=\frac{10,000}{50,000}=\boxed{0.2}$$APS=50,00010,000​=0.2​

Therefore, 20% of income is saved.

Marginal Propensity to Save (MPS)

The marginal propensity to save (MPS) is the proportion of additional income that is saved.

$$\boxed{MPS=\frac{\Delta S}{\Delta Y}}$$MPS=ΔYΔS​​

Example:

Income rises by ₹10,000 and saving rises by ₹3,000.

$$MPS=\frac{3,000}{10,000}=\boxed{0.3}$$MPS=10,0003,000​=0.3​

Of every additional ₹1 earned, ₹0.30 is saved.

Relationship Between Consumption and Saving

Since income is either consumed or saved:

$$\boxed{APC+APS=1}$$APC+APS=1​

$$\boxed{MPC+MPS=1}$$MPC+MPS=1​

For example, if MPC = 0.75:

$$MPS=1-0.75=\boxed{0.25}$$MPS=1−0.75=0.25​

Exam tip: APC and APS use total income and total expenditure. MPC and MPS use changes in income and expenditure.

Calculating Average and Marginal Propensities to Import

Average Propensity to Import (APM)

The average propensity to import (APM) is the proportion of total income spent on imports.

$$\boxed{APM=\frac{M}{Y}}$$APM=YM​​

Where:

• $M$M = total expenditure on imports
• $Y$Y = total income

Example:

National income = ₹500 billion

Import expenditure = ₹100 billion

$$APM=\frac{100}{500}=\boxed{0.2}$$APM=500100​=0.2​

The economy spends 20% of its income on imports under this measure.

Marginal Propensity to Import (MPM)

The marginal propensity to import (MPM) is the proportion of additional income spent on imports.

$$\boxed{MPM=\frac{\Delta M}{\Delta Y}}$$MPM=ΔYΔM​​

Example:

National income increases by ₹100 billion, while imports increase by ₹15 billion.

$$MPM=\frac{15}{100}=\boxed{0.15}$$MPM=10015​=0.15​

This means ₹0.15 of each additional ₹1 of income is spent on imports.

A higher MPM means a greater proportion of additional expenditure goes to foreign producers, reducing the domestic multiplier.

Calculating Average and Marginal Rates of Tax

Average Rate of Tax (ART)

The average rate of tax (ART) is the proportion of total income paid in tax.

$$\boxed{ART=\frac{T}{Y}\times100}$$ART=YT​×100​

Where:

• $T$T = total tax paid
• $Y$Y = total income

Example:

Income = ₹80,000

Tax paid = ₹12,000

$$ART=\frac{12,000}{80,000}\times100$$ART=80,00012,000​×100

$$\boxed{ART=15\%}$$ART=15%​

Marginal Rate of Tax (MRT)

The marginal rate of tax (MRT) is the proportion of additional income paid in additional tax.

$$\boxed{MRT=\frac{\Delta T}{\Delta Y}\times100}$$MRT=ΔYΔT​×100​

Example:

Income increases by ₹10,000 and tax paid increases by ₹2,000.

$$MRT=\frac{2,000}{10,000}\times100$$MRT=10,0002,000​×100

$$\boxed{MRT=20\%}$$MRT=20%​

The worker pays 20% of the additional income in tax.

Important distinction: ART measures tax as a proportion of total income. MRT measures tax on additional income. They need not be equal.

National Income Determination Using AD and the Income Approach

Aggregate Demand and National Income

Aggregate demand (AD) is total planned expenditure on domestically produced goods and services in an economy at a given price level.

The components of aggregate demand are:

$$\boxed{AD=C+I+G+(X-M)}$$AD=C+I+G+(X−M)​

Where:

• $C$C = consumption
• $I$I = investment
• $G$G = government spending on goods and services
• $X$X = exports
• $M$M = imports

In the simple Keynesian model, equilibrium national income occurs where planned aggregate expenditure equals national output.

$$\boxed{Y=AD}$$Y=AD​

If planned expenditure is greater than output:

→ Firms experience an unexpected fall in inventories.

→ Firms increase production.

→ Employment and income may rise.

If planned expenditure is less than output:

→ Unsold inventories accumulate.

→ Firms reduce production.

→ Employment and income may fall.

Determination of National Income: Income Approach

The income approach examines how income earned by households and firms changes as production and expenditure change.

In the simplified circular flow:

→ Firms produce goods and services.

→ Production generates income for workers and owners of factors of production.

→ Households spend part of their income on goods and services.

→ Firms receive revenue and use it to pay for further production.

National income is in equilibrium when the income generated by production is consistent with planned aggregate expenditure, with no unintended change in inventories.

In the full national accounts, the value of output, expenditure and income are equal in principle, subject to statistical discrepancies and accounting adjustments.

Equilibrium National Income Using the Multiplier

Example:

Suppose an economy has the following planned expenditure function:

$$AD=100+0.8Y$$AD=100+0.8Y

Here:

• ₹100 billion represents autonomous expenditure.
• $0.8Y$0.8Y represents induced expenditure, which changes with national income.

At equilibrium:

$$Y=AD$$Y=AD

Therefore:

$$Y=100+0.8Y$$Y=100+0.8Y

Rearrange:

$$Y-0.8Y=100$$Y−0.8Y=100

$$0.2Y=100$$0.2Y=100

$$\boxed{Y=₹500\text{ billion}}$$Y=₹500 billion​

The multiplier is:

$$k=\frac{1}{1-MPC} =\frac{1}{1-0.8} =\boxed{5}$$k=1−MPC1​=1−0.81​=5​

Autonomous expenditure is ₹100 billion. With the multiplier of 5, equilibrium national income is ₹500 billion.

Calculating the Effect of a Change in AD on National Income

Use the formula:

$$\boxed{\Delta Y=k\times\Delta AD}$$ΔY=k×ΔAD​

Example:

The multiplier is 4. Investment increases by ₹25 billion.

$$\Delta Y=4\times ₹25\text{ billion}$$ΔY=4×₹25 billion

$$\boxed{\Delta Y=₹100\text{ billion}}$$ΔY=₹100 billion​

National income increases by ₹100 billion, assuming the multiplier remains constant and there is sufficient capacity for output to respond.

If autonomous expenditure decreases by ₹25 billion instead:

$$\Delta Y=4\times(-₹25\text{ billion})$$ΔY=4×(−₹25 billion)

$$\boxed{\Delta Y=-₹100\text{ billion}}$$ΔY=−₹100 billion​

National income decreases by ₹100 billion.

Factors affecting the size of the multiplier

→ Higher MPC → more additional income is spent → larger multiplier.

→ Higher MPS → more income is saved → smaller multiplier.

→ Higher MRT → more additional income is paid in tax → smaller multiplier.

→ Higher MPM → more additional income is spent on imports → smaller multiplier.

→ Limited spare capacity → additional demand may increase prices more than real output, reducing the real-output response.

Components of Aggregate Demand and Their Determinants

Consumption Function: Autonomous and Induced Consumption

Consumption is expenditure by households on goods and services.

The consumption function shows the relationship between consumption expenditure and disposable income.

A simple consumption function is:

$$\boxed{C=a+bY_d}$$C=a+bYd​​

Where:

• $C$C = consumption expenditure
• $a$a = autonomous consumption
• $b$b = MPC
• $Y_d$Yd​ = disposable income

Autonomous consumption is consumption that takes place even when current disposable income is zero. Households may finance it through savings, borrowing or transfers.

Example: A household with no current income still buys essential food using savings.

Induced consumption is consumption that changes in response to a change in disposable income.

→ Disposable income rises → households have more money available → consumption usually rises.

Factors affecting consumption

• Disposable income: higher disposable income generally increases consumption.
• Wealth: higher property or financial wealth may increase confidence and spending.
• Interest rates: lower interest rates may encourage borrowing and spending.
• Consumer confidence: optimism about future income may increase current consumption.
• Availability of credit: easier access to loans may increase spending.
• Income distribution: a redistribution of income towards households with a higher MPC may increase total consumption.
• Expectations: expectations of future inflation or income changes can influence spending today.

Savings Function: Autonomous and Induced Saving

Saving is the part of disposable income that is not spent on consumption.

$$\boxed{S=Y_d-C}$$S=Yd​−C​

A simple savings function is:

$$\boxed{S=-a+(1-b)Y_d}$$S=−a+(1−b)Yd​​

Where:

• $-a$−a represents dissaving when disposable income is zero.
• $1-b$1−b is the MPS.

Autonomous saving is saving independent of current disposable income in the simplified model. It may be negative if households borrow or use existing savings to finance consumption when current income is low.

Induced saving changes as disposable income changes.

→ Disposable income rises → consumption usually rises, but not by the full increase in income → saving increases.

Factors affecting saving

• Disposable income: higher income generally allows more saving.
• Interest rates: higher returns on saving may encourage households to save more, although the overall effect depends on their circumstances.
• Confidence: uncertainty about the future may encourage precautionary saving.
• Age and life stage: people may save for retirement, education or housing.
• Wealth and debt: heavily indebted households may prioritise debt repayment.
• Expectations: anticipated future expenses may increase saving today.

Investment: Autonomous and Induced Investment

Investment in macroeconomics refers to expenditure on capital goods, such as machinery, equipment, factories and buildings. It does not simply mean buying shares or other existing financial assets.

Autonomous investment is investment that does not directly depend on current national income in the simplified model.

Examples include:

→ A firm replacing essential machinery.

→ Government-supported infrastructure projects.

→ Investment resulting from a new technology or a change in business expectations.

Induced investment changes in response to changes in income, demand or output.

→ National income rises → consumption and demand rise → firms need greater production capacity → firms may invest in additional machinery and factories.

Factors affecting investment

• Interest rates: lower borrowing costs can make investment projects more profitable.
• Business confidence: optimism about future demand encourages investment.
• Expected profitability: firms invest when expected returns exceed the costs and risks.
• Technological change: new technologies may create profitable investment opportunities.
• Capacity utilisation: firms operating near full capacity may need additional capital.
• Government policy: taxes, subsidies, regulations and infrastructure can influence investment decisions.
• Access to finance: firms need suitable funding to undertake projects.

The Accelerator

The accelerator principle explains how a change in demand or output can lead to a change in investment.

If firms need a larger capital stock to produce additional output, an increase in demand may lead to a proportionately larger change in investment.

Example:

A furniture manufacturer can produce 1,000 tables per month with its existing machinery. Demand rises to 1,300 tables per month, so the firm buys additional machines to expand capacity.

→ Higher demand → higher required output → additional capital needed → induced investment increases.

If demand falls:

→ Lower required output → spare capacity increases → firms may postpone or cancel investment.

The accelerator effect depends on the capital-output relationship, firms’ expectations, spare capacity and whether the change in demand is expected to persist.

Government Spending

Government spending is expenditure by the government on goods and services, such as schools, hospitals, roads, public transport and public-sector services.

Government spending is a component of aggregate demand.

How government spending affects national income

→ Government increases spending on road construction.

→ Construction firms receive additional orders.

→ Firms employ workers and buy materials.

→ Workers and suppliers receive additional income.

→ They spend part of this income, generating further rounds of expenditure.

→ National income rises through the multiplier process.

Factors affecting government spending

• Economic conditions: the government may increase spending to support demand during a downturn.
• Public priorities: education, healthcare, defence and infrastructure needs influence spending.
• Tax revenue: higher revenue may make additional spending easier to finance.
• Borrowing costs and debt: high debt-servicing costs may limit spending.
• Political decisions: government priorities and election commitments can affect expenditure.

Government spending on goods and services directly enters AD. Transfer payments, such as pensions and unemployment benefits, are not themselves payments for current production and are not directly counted as government purchases in the AD formula. However, they can increase households’ disposable income and consumption.

Net Exports

Net exports are the value of exports minus the value of imports.

$$\boxed{\text{Net exports}=X-M}$$Net exports=X−M​

Exports are goods and services sold to other countries. Imports are goods and services purchased from other countries.

→ Higher exports, with imports unchanged → net exports increase → AD increases.

→ Higher imports, with exports unchanged → net exports decrease → AD decreases.

Factors affecting net exports

• Overseas income: stronger economic growth abroad may increase demand for exports.
• Domestic income: higher domestic income may increase demand for imports.
• Exchange rates: a depreciation may make exports cheaper to foreign buyers and imports more expensive to domestic buyers, although the effect depends on demand elasticities and contracts.
• Relative prices and inflation: domestic goods becoming more expensive relative to foreign goods may reduce export competitiveness.
• Quality and preferences: better-quality products or changing consumer tastes can affect export demand.
• Trade barriers: tariffs, quotas and regulations can affect exports and imports.
• Competitiveness: productivity, production costs and reliability influence international sales.

Full Employment and Equilibrium National Income

Full Employment Level of National Income

The full employment level of national income is the level of real national output produced when the economy’s available labour resources are employed sustainably, apart from normal frictional and structural unemployment.

Full employment does not mean that every person has a job. Some people may be temporarily between jobs, retraining or unable to find work that matches their skills.

At full employment:

→ Most available resources are being used.

→ There is limited spare productive capacity.

→ A further increase in AD may create more pressure on prices if output cannot increase significantly.

Equilibrium Level of National Income

The equilibrium level of national income occurs where planned aggregate expenditure equals national output.

$$\boxed{Y=AD}$$Y=AD​

Equilibrium can occur below, at or above the full employment level of national income in the short-run Keynesian model.

• Equilibrium below full employment → the economy has unused resources and cyclical unemployment may exist.
• Equilibrium at full employment → planned spending is consistent with sustainable full-employment output.
• Equilibrium above full-employment output in a simplified expenditure model → spending exceeds sustainable productive capacity, creating upward pressure on prices.

Deflationary Gap

A deflationary gap occurs when equilibrium national income is below the full employment level of national income because aggregate demand is insufficient to purchase the output that could be produced at full employment.

→ AD is too low → firms experience weak sales and may accumulate unwanted inventories → production falls → employment and income fall → consumption falls further.

This can result in cyclical unemployment and unused productive capacity.

Example:

An economy could sustainably produce ₹1,000 billion of output at full employment, but equilibrium national income is only ₹850 billion.

$$\text{Deflationary gap}=₹1,000-₹850$$Deflationary gap=₹1,000−₹850

$$\boxed{\text{Deflationary gap}=₹150\text{ billion}}$$Deflationary gap=₹150 billion​

The economy is operating below its full-employment level of output.

Possible policies to reduce a deflationary gap

→ Increase government spending → AD rises → the multiplier may increase national income.

→ Reduce taxes → disposable income may rise → consumption may increase.

→ Lower interest rates, where appropriate → borrowing and investment may increase.

The effectiveness of these policies depends on confidence, spare capacity, time lags, leakages and the wider economic conditions.

Inflationary Gap

An inflationary gap occurs when planned aggregate demand at full-employment output exceeds the value of output that the economy can sustainably produce at that level.

→ AD rises beyond the economy’s productive capacity → firms face capacity constraints and labour shortages → costs and prices may rise → inflationary pressure increases.

In the simplified Keynesian expenditure model, this can be represented by planned expenditure exceeding full-employment output.

Example:

Full-employment national income is ₹1,000 billion, while planned aggregate expenditure at that income is ₹1,100 billion.

$$\text{Inflationary gap}=₹1,100-₹1,000$$Inflationary gap=₹1,100−₹1,000

$$\boxed{\text{Inflationary gap}=₹100\text{ billion}}$$Inflationary gap=₹100 billion​

This indicates excess planned spending relative to sustainable output at full employment. The gap is not necessarily equal to the eventual increase in the price level.

Possible policies to reduce an inflationary gap

→ Reduce government spending → AD falls.

→ Increase taxes → disposable income and consumption may fall.

→ Increase interest rates → borrowing, consumption and investment may decrease.

These policies may reduce inflationary pressure but can also slow economic growth and increase unemployment if demand falls too far.

Equilibrium and Full Employment: Key Comparison

Feature	Deflationary gap	Inflationary gap
AD relative to full-employment output	Insufficient	Excessive
Equilibrium national income	Below full employment	Spending pressure exceeds sustainable full-employment output
Resource use	Unused capacity	Capacity constraints
Likely problem	Cyclical unemployment	Inflationary pressure
Possible policy response	Expansionary policy	Contractionary policy

Final exam distinction: Equilibrium national income is where planned AD equals output. Full-employment national income is the level of output the economy can sustainably produce when resources are employed at normal full-employment levels. The two are not automatically equal.