Revision: Introductory Macroeconomics >> Determination of Income and Employment Economics Commerce (English Medium) Class 12 CBSE

• "Investment refers to the increment of capital equipment." — J.M. Keynes
• "By investment we do not mean the purchase of existing paper securities, bonds, debentures or equities, but the purchase of new factories, machines and the like". — Stonier and Hague
• "Investment expenditure includes expenditure for producer’s durable equipment, new construction and the change in inventories." — Peterson

The ratio of the total increment in equilibrium value of final goods output to the initial increment in autonomous expenditure is called the investment multiplier of the economy.

If all the people in an economy increase the proportion they save (mps increases), the total savings of the economy will not increase - they will remain the same or even decrease. This is known as the Paradox of Thrift.

Aggregate demand (AD) is the total planned spending on domestically produced final goods and services in an economy during a given period.

AD = C + I + G + (X − M)

Where:

• AD: Aggregate demand or aggregate expenditure (total planned spending).
• C: Desired consumption expenditure by households.
• I: Desired investment expenditure by firms.
• G: Desired government expenditure on goods and services.
• X: Exports of goods and services (what foreigners buy from us).
• M: Imports of goods and services (what we buy from other countries).
• (X – M): Net exports (exports minus imports).

In a simple closed economy (no government and foreign sector):

AD = C + I

Consumption and investment have different determinants and are studied separately.

\[C=\bar{C}+cY\]

• Ratio of total consumption to total income at a given level of income.

\[APC=\frac{C}{Y}\]

• Ratio of total saving to total income at a given level of income.

\[APS=\frac{S}{Y}\]

• Saving is the part of income that is not consumed.

Since,

\[S = Y − C\]

then,

\[s = 1 − c\]

• Change in consumption due to a unit change in income.
• Value always lies between 0 and 1 (inclusive).

\[MPC=c=\frac{\Delta C}{\Delta Y}\]

• Change in saving due to a unit change in income.
• MPC and MPS together always equal 1.

\[MPS=s=\frac{\Delta S}{\Delta Y}\]

P_I = `I / Y`
PI = Propensity to invest, I = Aggregate Investment, Y = Aggregate Income

The relationship between investment and the rate of interest can be written as:

I = f(r)

Here:

• I = Investment, the planned amount of investment; it is the dependent variable.​
• r = Rate of interest; it is the independent variable that influences investment.​

This notation means that the level of investment depends on the rate of interest.

AD = C + I

Where:

• AD = Ex-ante Aggregate Demand
• C = Ex-ante Consumption Expenditure
• I = Ex-ante Investment Expenditure

\[\overline{A}=\overline{CD}+\overline{I}\]

\[Y=\overline{A}+cY\]

Where:

• \[\bar A\] = Total Autonomous Expenditure

\[Y_d\] ​= Y − T

Where:

• \[Y_d\] = Disposable Income
• Y = National Income
• T = Taxes

\[Y=\overline{C}+\overline{I}+G+c(Y-T)\]

Where:

• G = Government Expenditure
• T = Taxes

G − cT becomes part of autonomous expenditure and does not change the basic analysis. For simplicity, the chapter continues with the two-sector model.

\[Y=\overline{C}+\overline{I}+cY\]

Where:

• Y = Planned (Ex-ante) Output
• \[\bar C\] = Autonomous Consumption
• \[\bar I\] = Autonomous Investment
• c = Marginal Propensity to Consume (MPC)

\[\frac{\Delta Y}{\Delta\bar{A}}=\frac{1}{1-c}=\frac{1}{s}\]

where,

• ΔY: Total increment in equilibrium value of final goods output (national income).
• ΔĀ: Initial increment in autonomous expenditure (e.g., ΔĪ).
• c: MPC (Marginal Propensity to Consume).
• s: MPS (Marginal Propensity to Save), equal to 1 − c.

\[Y^*=\frac{\bar{A}}{1-mpc}\]

where,

• \[\overline{A}\] = Autonomous expenditure
• \[Y^∗\] = Equilibrium income
• mpc = Marginal propensity to consume

\[\Delta Y=\frac{\Delta A}{1-mpc}\]

where,

• \[\Delta A\] = Change in autonomous expenditure
• mpc = Marginal propensity to consume

mpc + mps = 1

where,

• mpc = Marginal propensity to consume
• mps = Marginal propensity to save

• Short‑run national income in Keynesian theory is determined by desired aggregate demand or aggregate spending.
• Aggregate demand can be viewed as desired (ex‑ante) demand and effective (ex‑post) demand.
• In a two‑sector closed economy, AD consists of consumption and investment: AD = C + I.
• In a four‑sector economy, AD = C + I + G + (X – M).
• Ex‑ante and ex‑post concepts apply to macro variables like consumption, investment and output and are essential for understanding income determination.

• The consumption function \[C=\bar{C}+cY\] shows that consumption consists of autonomous consumption and induced consumption.
• Autonomous consumption \[\overline{C}\] is the minimum consumption even when income is zero.
• Induced consumption (\[cY\]) depends on income.
• MPC measures how much of an additional income is spent; its value always lies between 0 and 1 (inclusive).
• MPS measures how much of an additional income is saved; MPC + MPS = 1.
• \[APC=\frac{C}{Y}\] and APS = \[APS=\frac{S}{Y}\] measure average spending and saving relative to income.
• The 45° line is the reference line where income equals consumption and saving is zero.

• Economic investment = addition to physical capital + change in inventories — NOT buying shares/bonds​
• Autonomous investment is income-inelastic, welfare-driven, mostly by government; drawn as a horizontal line​
• Induced investment is income-elastic, profit-driven, mostly private; drawn as an upward-sloping line​
• Gross Investment = Net Investment + Depreciation; net investment positive means capital accumulation
• Ex-ante = planned; Ex-post = actual; equilibrium requires ex-ante S = ex-ante I​
• Investment function I = f(r) is downward-sloping — higher interest means less investment​
• Invest when MEI > Rate of Interest; stop when MEI = Rate of Interest​

• In a two-sector economy, AD = C + I.
• Equilibrium occurs when planned output equals planned aggregate demand.
• Autonomous expenditure = Autonomous Consumption + Autonomous investment.
• Inventory investment arises due to differences between planned and actual sales.
• Disposable Income = Y − T.
• Without indirect taxes and subsidies, GDP = National Income.

• Macroeconomic equilibrium is studied in two stages - fixed price first, variable price next.
• Microeconomics determines price and quantity simultaneously; macroeconomics separates the two stages.
• Fixed price is justified by the existence of unused resources in the economy.
• With unused resources, marginal cost does not rise, so price stays constant despite output changes.
• The fixed price assumption is temporary and will be dropped at Stage 2.

• Consumption function is a straight line with intercept \[\overline{C}\] and slope c.
• Investment is autonomous and constant at all income levels: \[I = \overline{I}\]
• Aggregate demand is the vertical sum of consumption and investment and is parallel to the consumption function.
• Aggregate supply with fixed price level is represented by a 45° line, where output supplied equals GDP.
• Equilibrium occurs where ex ante aggregate demand equals ex ante aggregate supply, giving equilibrium income OY₁.
• Algebraically, \[Y=\frac{\bar{C}+\bar{I}}{1-c}\]

• Equilibrium income is where the AD curve cuts the 45° line (AD = Output).
• An autonomous rise in investment shifts the AD curve upward, creating excess demand.
• Firms increase output in response to excess demand, raising income.
• The final increase in equilibrium income is greater than the initial increase in autonomous expenditure, indicating a multiplier effect.

• Investment Multiplier measures the ratio of the increase in equilibrium income to the initial increase in autonomous expenditure.
• An increase in autonomous expenditure raises income, consumption, and output through repeated rounds of spending.
• The size of the multiplier depends on the Marginal Propensity to Consume (MPC) - higher MPC results in a larger multiplier.
• Total increase in income is greater than the initial increase in autonomous expenditure due to the multiplier effect.
• Investment Multiplier Formula: \[K=\frac{\Delta Y}{\Delta\bar{A}}=\frac{1}{1-c}=\frac{1}{s}\]

• The Paradox of Thrift states that higher individual saving does not lead to higher aggregate savings in the economy.
• When mps rises (mpc falls), equilibrium income falls through the multiplier chain.
• The multiplier chain is an infinite convergent geometric series.
• Aggregate savings remained at 10 in both equilibria, confirming the paradox.
• This is a Keynesian concept under the topic of Income and Employment Determination.

• Equilibrium output decides employment, given other factors.
• Y = AD does not guarantee full employment.
• Full employment income means all factors are fully used.
• Equilibrium income can exist with unemployment.
• Output less than full employment → deficient demand → prices fall in long run.
• Output more than full employment → excess demand → prices rise in long run.