Chapter 3 — Determination Of Income And Employment

Fig 1 — Educational Diagram: Introduction and Basic Assumptions

What the topic deals with

This topic introduces Keynesʼ short‑run theory of determination of national income and employment. It explains how aggregate demand (effective demand) — the total planned spending by households and firms — determines the level of output and employment in the economy when prices are assumed fixed in the short run.

Key concepts

• Effective demand: Planned aggregate expenditure at different levels of output. Equilibrium output occurs where planned aggregate demand equals actual output produced.
• Aggregate demand in the simple model: AD = C + I (no government, no foreign sector).
• Consumption function: Consumption (C) depends on income (Y): C = a + bY, where a = autonomous consumption, b = marginal propensity to consume (MPC).
• Equilibrium condition: Output (Y) is in equilibrium when Y = C + I. Using the consumption function this gives Y = a + bY + I ⇒ Y(1 − b) = a + I ⇒ Y* = (a + I)/(1 − b).
• Savings‑investment identity: At equilibrium planned saving equals planned investment (S = I). Savings S = Y − C.
• Multiplier effect: A change in autonomous spending (for example, investment) leads to a multiplied change in equilibrium income. Multiplier k = 1/(1 − MPC) = 1/MPS.

Basic assumptions of the simple Keynesian model

• Closed economy: no government and no foreign trade (two‑sector model: households and firms).
• Price level is fixed (short‑run), so changes in aggregate demand change output and employment, not prices.
• Investment is autonomous (given) and does not depend on current income in the basic model.
• Propensities to consume are stable: MPC (b) is constant and 0 < b < 1.
• Wages and other input prices are sticky in the short run, so output adjusts before prices do.
• Factors of production (labour and capital) are available but not necessarily fully employed — equilibrium may occur with unemployment.

Why these assumptions matter

These simplifying assumptions let us focus on how planned spending determines national income. Removing or relaxing assumptions (adding government, taxes, imports, price adjustment) leads to more complex but more realistic models.

Fig 2 — Educational Diagram: Aggregate Demand and Aggregate Supply

Aggregate Demand (AD)

Aggregate Demand is the total demand for final goods and services in an economy at a given overall price level and in a given period. It shows the relationship between the price level and the quantity of real national output (real GDP) demanded. In functional form, AD is the sum of its components: consumption, investment, government expenditure and net exports.

Key properties and determinants of AD:

• AD curve slopes downward: a higher price level reduces the real value of money balances, raises interest rates and reduces investment and consumption; it also makes domestic goods relatively expensive, lowering net exports.
• Components that shift AD (at every price level): changes in fiscal policy (G or taxes), monetary policy (affecting investment), consumer confidence (consumption), business expectations (investment), foreign income and exchange rates (net exports).

Aggregate Supply (AS)

Aggregate Supply is the total quantity of goods and services that firms are willing and able to produce at different price levels in a given period. In the short run AS is generally upward sloping because higher prices for outputs (with some sticky wages/prices) increase firms' profits and encourage more production. In the long run classical AS is vertical at the economy’s potential (full‑employment) output.

Determinants and shifts of AS:

• Factors that shift AS: changes in resource availability (labour, capital), technology, input prices (wages, energy), supply shocks (natural disasters), and institutional changes.
• Short-run AS may be divided into ranges (Keynesian: flat at low output; intermediate: upward sloping; classical: vertical near full employment) to show different responses of output and prices to demand changes.

Equilibrium of Income and Employment (AD = AS)

Equilibrium real output (income) and the price level are determined where the AD and AS curves intersect. A rightward shift of AD raises output and the price level (depending on AS slope). A leftward shift of AS (negative supply shock) raises price level and reduces output (stagflation).

Key implications

• Demand-side policies (fiscal/monetary) shift AD and can be used to stabilize output and employment.
• Supply-side policies (education, technology, labor market reforms) shift AS and raise potential output without inflationary pressure.

Simple algebraic view (short-run Keynesian two-sector model)

• Consumption function: C = a + cY (a = autonomous consumption; c = MPC).
• Aggregate demand (closed economy, no government): AD = C + I.
• Equilibrium (Y = AD) gives Y* = (a + I) / (1 - c). Increase in autonomous spending ΔI raises equilibrium output by ΔY = (1 / (1 - c)) × ΔI (investment multiplier).

Fig 3 — Educational Diagram: Consumption Function

Definition: The consumption function expresses the functional relationship between aggregate consumption expenditure (C) and aggregate disposable income (Yd or simply Y). It shows how much of an additional unit of income households are likely to spend on consumption.

Key components:

• Autonomous consumption (a): The portion of consumption that does not depend on current income (consumption at zero income). It is financed by savings, borrowing or transfers.
• Induced consumption (bY): The income-dependent part of consumption that changes when income changes. Its slope equals the marginal propensity to consume (MPC).

Standard (linear) form: C = a + bY (or C = C0 + cYd). Here, a (or C0) is autonomous consumption and b (or c) is MPC.

Behavioral law (Keynes): As income increases, consumption increases, but by a smaller amount — i.e., households save a part of any additional income. Hence 0 < MPC < 1.

Relation with saving: Saving is the part of income not consumed: S = Y - C. Using the linear consumption function, S = -a + (1 - b)Y. This implies negative saving (dissaving) at very low incomes until income is high enough to offset autonomous consumption.

Important properties:

• MPC = change in consumption / change in income = ∂C/∂Y = b (0 < b < 1).
• Average propensity to consume (APC) = C/Y = (a/Y) + b; APC falls as income rises because a/Y declines.
• MPS (marginal propensity to save) = 1 - MPC.
• The consumption function is upward sloping and intersects the vertical axis at autonomous consumption a.

Assumptions (for the simple linear form): tastes, prices and interest rates are constant; income is the main determinant of consumption; MPC is constant over the relevant range.

Limitations: In reality consumption depends on many factors (wealth, expectations, credit, interest rates, taxes, social norms), and the MPC may change with income level or over time. The linear function is a simplification used for analysis.

Connection to the multiplier: The Keynesian income multiplier depends on MPC: multiplier k = 1/(1 - MPC). A higher MPC yields a larger multiplier.

Fig 4 — Educational Diagram: Propensity to Consume

Definition: Propensity to consume is the tendency of households to spend a part of their income on consumption. It shows how much of a given increase in income will be used for consumption and how much will be saved.

Two key measures:

• Average Propensity to Consume (APC) = total consumption (C) divided by total income (Y). It shows the proportion of total income spent on consumption: APC = C/Y.
• Marginal Propensity to Consume (MPC) = change in consumption divided by change in income. It shows the portion of an additional unit of income that is consumed: MPC = ΔC/ΔY.

Keynesian consumption function: C = a + bYd, where a is autonomous consumption (consumption when income is zero), b is the MPC (0 < b < 1), and Yd is disposable income. Induced consumption = bYd; autonomous consumption = a.

Relationships and properties:

• APC = C/Y = (a + bY)/Y = a/Y + b. As income increases, a/Y falls, so APC tends to decline and approaches b (MPC).
• MPC + MPS = 1, where MPS (marginal propensity to save) = ΔS/ΔY. (In a simple model without taxes and transfers.)
• 0 < MPC < 1 usually: consumption rises with income but by less than the increase in income. APC can be > 1 at low income levels if consumption exceeds current income (financed by borrowing or dissaving), but typically APC lies between 0 and 1 for steady states.

Economic interpretation: A higher MPC means that a larger fraction of any additional income will be spent, raising aggregate demand and stimulating output through the multiplier. APC indicates the average share of income devoted to consumption and helps identify saving behavior as income changes.

Factors influencing propensity to consume: income level, wealth, expectations about future income, interest rates (cost of borrowing and return on saving), fiscal policy (taxes and transfers), availability of credit, social norms and demographic structure.

Fig 5 — Educational Diagram: Saving Function and Propensity to Save

Saving function — definition: The saving function shows the relationship between saving (S) and national income (Y). In Keynesian analysis, if consumption (C) is C = a + bY (where a = autonomous consumption, b = MPC), then saving is the portion of income not consumed: S = Y − C.

Derivation: Using C = a + bY, we get S = Y − (a + bY) = −a + (1 − b)Y. Writing s = 1 − b (the marginal propensity to save), the saving function becomes S = −a + sY.

Interpretation of parameters: • −a is the vertical intercept (saving at zero income). Because a > 0 (autonomous consumption), S(0) = −a < 0 ⇒ dissaving at zero income. • s (0 < s < 1) is the slope of the saving function and equals the marginal propensity to save (MPS). A higher s means saving rises faster with income.

Propensity to save: • Marginal propensity to save (MPS): MPS = ΔS / ΔY = s = 1 − MPC. It measures how much of an additional unit of income is saved. • Average propensity to save (APS): APS = S / Y = (−a / Y) + s. APS varies with income (because of the −a/Y term) and approaches s as Y becomes large.

Key properties and economic implications: • At low income, S may be negative (dissaving) because households finance consumption out of past savings or borrow. • Saving is zero when S = 0 ⇒ Y = a / s. This is the income level at which households exactly consume their income (no saving, no dissaving). • Since MPC + MPS = 1, an increase in MPC reduces MPS and vice versa — important for multiplier effects on aggregate demand.

Summary: The saving function S = −a + sY links saving to income, with the intercept representing autonomous dissaving and the slope equal to MPS. APS falls with rising income toward MPS. Understanding these relationships helps explain consumption, saving behavior, and the fiscal or monetary policy impacts on aggregate demand.

Fig 6 — Educational Diagram: Investment

Definition: In macroeconomics (Class 12 context) investment means expenditure on production of capital goods and changes in inventories. It is the addition to the stock of real capital that increases future production capacity. Investment (I) is a component of aggregate demand: Y = C + I (in a closed economy without government and foreign trade).

Types of investment:

• Gross vs Net: Gross Investment = Net Investment + Depreciation. Net investment increases the stock of capital.
• Fixed vs Inventory: Fixed investment is spending on buildings, machinery, houses. Inventory investment is change in unsold stocks (can be planned or unplanned).
• Autonomous vs Induced: Autonomous investment is independent of current income (e.g. a policy-led public project). Induced investment depends on income/production (accelerator behaviour).
• Planned vs Unplanned: Planned investment is intended by firms. Unplanned investment arises when inventories change because actual sales differ from expected.

Key concepts used in the chapter:

• Investment as autonomous in the simple Keynesian model: In the basic goods-market model consumption is a function of income, C = a + bY, while investment is treated as autonomous (I = I¯). Equilibrium income satisfies Y = C(Y) + I¯.
• Multiplier effect: A change in autonomous investment produces a multiplied change in equilibrium income: ΔY = k × ΔI, where k = 1/(1 - MPC). Thus a rise in investment raises output and employment more than the initial rise.
• Interest sensitivity: In a more complete (IS) analysis investment is a decreasing function of the rate of interest r, e.g. I = I0 − br. Firms invest when expected returns exceed cost of funds.
• Marginal Efficiency of Capital (MEC): MEC is the expected rate of return on an additional unit of capital. Investment is undertaken when MEC ≥ market rate of interest. Formally MEC is the discount rate that equates the present value of expected returns to the cost of the capital good.

Role of investment in determination of income and employment:

• An increase in autonomous investment shifts aggregate expenditure upward, raising equilibrium output and employment via the multiplier.
• A decrease in investment (due to falling confidence or higher interest rates) reduces aggregate demand, output and employment; unplanned inventory accumulation signals firms to cut production and jobs.

Determinants of investment: rate of interest, business expectations/confidence, profits, level of income (demand), technological change, capacity utilization, government policy (subsidies/taxes), and cost of capital goods.

Summary: Investment is a central autonomous or partly interest-sensitive component of aggregate demand. Changes in investment generate multiplied changes in national income and employment. Understanding the types (autonomous/induced, planned/unplanned), the multiplier mechanism, and the interest/MEC link is essential for analysing fluctuations in output and jobs.

Fig 7 — Educational Diagram: Equilibrium Level of Income and Employment

What is equilibrium level of income and employment?

Equilibrium level of national income (Y_e) is the level of output/income at which planned aggregate expenditure equals actual output produced in the economy. At this point firms have no incentive to change output and employment: aggregate demand (AD) = aggregate supply (AS) or, in a simple closed private economy, planned consumption plus planned investment equals output (C + I = Y).

Two equivalent approaches

1) Aggregate demand — Aggregate supply (AD = AS): Plot aggregate expenditure (AE = C + I) against income (Y). Equilibrium is the intersection of AE and the 45° line (where AE = Y).

2) Saving — Investment (S = I): Because Y = C + S and Y = C + I, equilibrium requires S = I. When planned saving equals planned investment, desired spending equals output.

Key derivation (closed economy, no government):

Consumption function: C = C0 + cY (C0 = autonomous consumption, c = marginal propensity to consume, 0 < c < 1).

Equilibrium condition: Y = C + I = C0 + cY + I.

Solve for equilibrium income: Y(1 − c) = C0 + I → Y_e = (C0 + I) / (1 − c).

Here the denominator (1 − c) is the marginal propensity to save (MPS). The investment multiplier k = 1 / (1 − c) = 1 / MPS. So a change in autonomous investment ΔI produces ΔY = k × ΔI.

Stability and assumptions

If 0 < c < 1, the AE line has slope less than 45°, making equilibrium stable: any excess supply or demand induces movements back to equilibrium. Standard assumptions: fixed price level in the short run, given (autonomous) investment, fixed MPC, no external sector or government (unless extended).

Full employment vs underemployment

Equilibrium need not imply full employment. Keynes pointed out that equilibrium can occur at less than full employment because wages/prices may be sticky downward and investment insufficient to purchase full-capacity output.

Economic significance

Understanding equilibrium shows how shifts in autonomous spending (investment, government spending, exports) change income and employment via the multiplier. It explains why fiscal policy (e.g., spending increases) can raise output and reduce unemployment during demand shortfalls.

Fig 8 — Educational Diagram: Derivation of Equilibrium — Algebraic and Graphical Methods

Overview
In the Keynesian short‑run model (closed economy, no government or with government when specified), equilibrium level of income (output) is the level at which planned aggregate expenditure equals actual output produced. Two standard ways to derive equilibrium are:

• Algebraic method: Solve the equation Y = AD (or Y = AE), where AD/AE is aggregate demand/planned aggregate expenditure.
• Graphical method: Use the Keynesian cross (45° line diagram) or the S–I (saving–investment) diagram to show the intersection that determines equilibrium output.

Basic building blocks

• Consumption function (simple form): C = a + bY (or C = a + b(Y - T) with taxes). Here a = autonomous consumption, b = MPC (marginal propensity to consume).
• Investment I = I0 (assumed autonomous/constant in the simple model).
• Aggregate expenditure (AE) in a closed economy without government: AE = C + I = a + bY + I0.

Algebraic derivation (simple model without government)

1. Equilibrium condition: Y = AE = a + bY + I0.
2. Rearrange: Y - bY = a + I0 → Y(1 - b) = a + I0.
3. Thus equilibrium income: Y* = (a + I0) / (1 - b).

Interpretation: (a + I0) is total autonomous spending; 1/(1 - b) is the multiplier that magnifies autonomous spending into equilibrium income.

Alternative algebraic route: Savings–Investment approach

• Saving: S = Y - C = Y - (a + bY) = -a + (1 - b)Y.
• Equilibrium requires planned investment = planned saving: I0 = S → I0 = -a + (1 - b)Y.
• Solving gives the same Y*: Y* = (a + I0) / (1 - b).

With government (lump‑sum taxes T and government spending G)
Consumption: C = a + b(Y - T). Aggregate demand: AE = C + I0 + G = a + b(Y - T) + I0 + G. Equilibrium Y solves: Y = a + b(Y - T) + I0 + G → Y(1 - b) = a - bT + I0 + G → Y* = [a - bT + I0 + G] / (1 - b).

Stability intuition
If actual output Y is greater than planned spending AE, firms accumulate unintended inventories and cut production → Y falls. If Y < AE, firms draw down inventories and increase production → Y rises. Movement continues until Y = AE.

Fig 9 — Educational Diagram: Investment Multiplier

Definition: The investment multiplier is the ratio of the change in national income (ΔY) to an initial autonomous change in investment (ΔI). It shows how an initial increase in autonomous spending produces a larger final change in aggregate income.

Key idea and origin: Introduced by R.F. Kahn and developed by J.M. Keynes. When an autonomous injection of spending (for example, government investment) raises income, part of that additional income is consumed, causing further rounds of income and consumption. The total effect is the sum of these rounds.

Simple derivation (closed economy, no taxes or imports): Let consumption function be C = a + bY where a is autonomous consumption and b = MPC (marginal propensity to consume). National income identity (with autonomous investment I):

Y = C + I = a + bY + I

Rearrange: Y(1 - b) = a + I → a change in autonomous investment ΔI leads to

ΔY = 1/(1 - b) × ΔI.

Hence the simple multiplier k = 1/(1 - MPC) = 1/MPS.

Successive-round explanation: If MPC = b, an initial injection ΔI raises income by ΔI (round 0). Households consume b·ΔI (round 1), raising income by that amount; next round consumption is b^2·ΔI, etc. Total ΔY = ΔI [1 + b + b^2 + ...] = ΔI / (1 - b).

Generalised multiplier (with taxes and imports): If there is a marginal tax rate t and marginal propensity to import m, and savings s = 1 - c, the denominator must reflect all leakages. With induced consumption C = c(1 - t)Y and imports mY, the multiplier becomes:

k = 1 / [1 - c(1 - t) + m] = 1 / [s + c·t + m].

Assumptions: constant MPC, prices and interest rates fixed (no crowding out), idle resources (no supply constraints), autonomous change in spending, no time lags in consumption response, stable propensity to import and tax rates if included.

Implications: A higher MPC (or lower MPS) raises the multiplier. Leakages (savings, taxes, imports) reduce the multiplier. Multipliers justify fiscal stimulus: a relatively small autonomous increase in spending can generate a larger increase in national income when conditions permit.

Fig 10 — Educational Diagram: Assumptions, Importance and Limitations of the Multiplier

What is the multiplier? The multiplier shows how a change in autonomous expenditure (typically investment or government spending) produces a larger change in aggregate income (national output). If k is the multiplier and ΔA is the change in autonomous spending, then the total change in income ΔY = k × ΔA.

Derivation (simple closed economy, no taxes, no imports): An initial increase in autonomous spending ΔA raises income by ΔA in the first round. Households consume a fraction (MPC) of the extra income, producing further income in the next round, and so on. This gives a geometric series:

ΔY = ΔA + MPC·ΔA + MPC^2·ΔA + ... = ΔA(1 + MPC + MPC^2 + ... ) = ΔA / (1 − MPC).

Key formula (simple model): k = 1 / (1 − MPC) = 1 / MPS.

Generalized formula (with leakages): When saving (MPS), taxes (MPT) and imports (MPM) are present, the effective marginal leakage is the sum of these propensities. The multiplier becomes:

k = 1 / (MPS + MPT + MPM).

Assumptions of the multiplier

• Economy has unemployed resources and excess capacity so output can expand without driving up prices (fixed price level).
• MPC (marginal propensity to consume) is constant during the process.
• No supply-side constraints or bottlenecks; firms can meet increased demand.
• No crowding out: interest rates and private investment are unaffected by the policy-induced demand change.
• Autonomous change is exogenous and sustained long enough for rounds of spending to occur.
• For the simple formula: closed economy, no taxes and no imports (or leakages are constant and known).
• No time lags or adaptive expectations that alter consumption/investment behavior over rounds.

Importance (why the multiplier matters)

• Policy design: Helps governments estimate how much fiscal stimulus (ΔG or ΔI) is needed to achieve a target change in national income.
• Explains amplification: Small autonomous changes (investment, government spending, exports) can have proportionally larger effects on aggregate demand and employment.
• Employment: By showing how demand increases output, the multiplier explains how fiscal actions can reduce unemployment.
• Macro forecasting: Useful for short-run policy analysis and for understanding business cycle magnitudes.
• Targets redistribution: Knowing MPC differences across income groups helps design transfers that yield higher multipliers (poorer households typically have higher MPCs).

Limitations (why the real-world multiplier may be smaller or unreliable)

• MPC is not constant. It varies across income groups and over time (e.g., households may save more when uncertain).
• Leakages (savings, taxes, imports) reduce the multiplier; in open economies with high imports the multiplier is much smaller.
• Price-level changes and inflation: If output nears capacity, higher demand raises prices rather than real output, reducing the real multiplier.
• Crowding out: Fiscal expansion may raise interest rates, reducing private investment and offsetting part of the stimulus.
• Time lags and expectations: Delays in implementing policy or changes in expectations can weaken and delay the multiplier effect.
• Supply constraints and structural bottlenecks can prevent increased demand from translating into higher output and employment.
• Fiscal sustainability: Repeated use of deficit-financed spending can raise debt and future taxes, changing behavior and lowering future multipliers.

Summary: The multiplier is a powerful conceptual tool showing how autonomous spending transmits into larger changes in income, but its quantitative size depends on real-world features—MPC, taxes, imports, interest rates, capacity, and expectations. Policymakers must account for these limitations when using multipliers to design fiscal interventions.

Fig 11 — Educational Diagram: Multiplier in Extended Models (Government and External Sector)

What is the multiplier in extended models?

The multiplier shows how a change in autonomous spending (investment, government spending, exports, etc.) causes a larger change in national income. In extended models that include government and the external sector, additional leakages — taxes and imports — reduce the size of the multiplier.

Key idea and derivation (compact)

Start with the income identity for an open economy with taxes:

Y = C + I + G + (X - M)

with C = C0 + c(Y - T) and T = T0 + tY, and M = mY.

Substitute to get (after rearranging):

Y[1 - c(1 - t) + m] = Autonomous spending (A) = C0 - cT0 + I + G + X

Therefore the marginal propensity to withdraw (MPW) is

MPW = 1 - c(1 - t) + m

and the multiplier (k) is the reciprocal of MPW:

k = 1 / [1 - c(1 - t) + m]

This gives the change in income produced by a change in autonomous spending ΔA:

ΔY = k · ΔA

Interpretation of terms

• c = marginal propensity to consume (MPC)
• t = marginal (proportional) tax rate; higher t reduces consumption from additional income
• m = marginal propensity to import (MPM); higher m leaks demand abroad
• When taxes are lump-sum (T = T0 only) and there is no external sector (m = 0), the formula reduces to the simple multiplier k = 1 / (1 - c)

Alternative expression of MPW as sum of leakages

MPW = MPS + MPT + MPM, where

• MPS = change in savings / change in income = (1 - t)(1 - c)
• MPT = change in taxes / change in income = t
• MPM = change in imports / change in income = m

Summing these gives MPW = (1 - t)(1 - c) + t + m = 1 - c(1 - t) + m (same as above).

Consequences

• Higher tax rate (t) or higher imports (m) reduce the multiplier.
• Balanced-budget changes: for a lump-sum tax increase equal to an increase in G, the balanced-budget multiplier equals 1 in the simple closed-economy case (because ΔY = ΔG). With imports or proportional taxes the effect is smaller.
• Export expansion (ΔX > 0) raises income via the multiplier; import leakages reduce how large that rise will be.

Fig 12 — Educational Diagram: Stability of Equilibrium and Adjustments

What is equilibrium? In the Keynesian goods market an equilibrium level of income (Y*) is the level at which planned aggregate expenditure (AE) equals actual output (Y). In other words: planned spending = output produced, so firms have no incentive to change production.

Equilibrium condition
Y = C + I + G + NX, where C is consumption, I investment (autonomous), G government spending and NX net exports. With a simple consumption function C = a + cY (or C = a + cYd when taxes exist), equilibrium can be written and solved for Y*.

Stability of equilibrium — intuitive (inventory adjustment)
If output exceeds planned expenditure (Y > AE), firms sell less than they produce and inventories accumulate. Facing rising inventories, firms cut production and income falls until Y declines to the point where AE = Y. Conversely, if output is below planned expenditure (Y < AE), inventories fall and firms raise production and income until Y increases to equilibrium. When these automatic inventory-based adjustments push Y toward Y*, the equilibrium is stable.

Stability — algebraic/dynamic view
Take the simple dynamic rule: firms set next period's output equal to current planned expenditure so
Y_{t+1} = C(Y_t) + A, where A = I + G + NX (autonomous spending) and C(Y_t) = a + cY_t.

Subtract the steady-state Y* from both sides and you get
Y_{t+1} - Y* = c (Y_t - Y*).

This recurrence shows the gap from equilibrium is multiplied each period by c (the marginal propensity to consume, MPC). If |c| < 1 (in practice 0 < c < 1), the gap shrinks over time and the equilibrium is stable. If |c| > 1 the gap would grow and equilibrium would be unstable (not realistic for MPC).

Why MPC < 1 ensures stability
Since MPC (c) is the fraction of additional income spent on consumption, it lies between 0 and 1. Therefore future adjustments are smaller than current gaps and the economy converges to equilibrium. Mathematically stability requires |dAE/dY| < 1, i.e. MPC < 1.

Equilibrium in terms of leakages and injections
Another characterization: equilibrium in the circular flow occurs when total leakages = total injections. Leakages = S + T + M (saving, taxes, imports). Injections = I + G + X (investment, government spending, exports). So equilibrium: S + T + M = I + G + X. If leakages exceed injections aggregate demand falls and income falls until equality is restored; if injections exceed leakages income rises. Stability requires that adjustments in income change leakages/injections in a way that closes the gap (marginal propensities ensure this).

Underemployment equilibrium
Keynesian equilibrium may occur at less than full employment. Stability only means the economy tends to stay at that equilibrium (because of the adjustment process described); it does not guarantee full employment.

Summary of the mechanism

• If Y > AE → unsold inventories rise → firms cut output → Y falls toward Y*.
• If Y < AE → inventories fall → firms increase output → Y rises toward Y*.
• Algebraically, convergence requires MPC (c) < 1 (true in practice), so |c| < 1 ensures stability.

Fig 13 — Educational Diagram: Numerical Problems and Applications

What the topic covers
Numerical problems in the chapter "Determination of Income and Employment" apply the simple Keynesian model (closed economy without government) to compute equilibrium national income, saving, and the effect of changes in autonomous spending. The model uses a linear consumption function and a constant level of autonomous investment.

Basic steps to solve numerical problems

• Write the consumption function: C = a + bY (where a = autonomous consumption, b = marginal propensity to consume, 0 < b < 1).
• Write equilibrium condition: Y = C + I (aggregate output equals aggregate demand; I is autonomous investment).
• Substitute C into equilibrium and solve for Y: Y = a + bY + I → Y(1 - b) = a + I → Y = (a + I)/(1 - b).
• Find saving: S = Y - C = Y - (a + bY) = -a + (1 - b)Y. Note that 1 - b is the MPS (marginal propensity to save).
• Use the investment multiplier: k = 1/(1 - b). A change in autonomous investment ΔI causes a change in equilibrium income ΔY = k × ΔI.

Key ideas to remember

• Autonomous components (a, I) shift the aggregate expenditure line up or down; induced consumption depends on income via b.
• The 45-degree (Y = AE) diagram is useful: equilibrium income is where aggregate expenditure (C+I) intersects the 45-degree line.
• Multiplier is larger when MPC (b) is higher because more of each rupee earned is spent again.

Common numerical tasks

• Find equilibrium income given a, b and I.
• Compute saving function and break-even income (where S = 0).
• Calculate the multiplier and the change in equilibrium income following a change in autonomous investment or consumption.
• Illustrate results on the Keynesian cross: show initial equilibrium and the new equilibrium after a shift in autonomous spending.

Fig 14 — Educational Diagram: Key Terms and Definitions

This section explains the core terms used in the Keynesian short‑run model of determination of income and employment (two‑sector closed economy). The model is built around the income‑expenditure relationship Y = C + I and shows how aggregate demand determines equilibrium output and employment.

Aggregate Demand (AD): Total planned expenditure on final goods and services in the economy at a given level of income. In a two‑sector model, AD = C + I.

Aggregate Supply (AS): Total output (income) produced in the economy at a given level of prices. In the short run Keynesian model, AS is identified with actual income (Y).

Effective Demand: The level of aggregate demand (AD) at which firms decide the level of output to produce. Equilibrium output is determined at the point of effective demand where planned expenditure equals output.

Consumption Function: The relationship between consumption expenditure (C) and national income (Y). The linear form used in Class 12 is C = a + bY, where:

• a = autonomous consumption (consumption when Y = 0)
• b = marginal propensity to consume (MPC), the slope of the consumption function

Autonomous Consumption: The part of consumption which does not depend on current income (funded by past savings, borrowing, transfers). It is the intercept 'a' in C = a + bY.

Induced Consumption: The portion of consumption that changes with income, equal to bY in the linear function.

Marginal Propensity to Consume (MPC): MPC = ΔC / ΔY. It is the fraction of an additional rupee of income that is spent on consumption. 0 < MPC < 1.

Marginal Propensity to Save (MPS): MPS = ΔS / ΔY = 1 − MPC. It is the fraction of an additional rupee of income that is saved.

Average Propensity to Consume (APC): APC = C / Y. It shows the average share of income spent on consumption.

Average Propensity to Save (APS): APS = S / Y = 1 − APC.

Saving Function: Relationship between saving (S) and income. From C = a + bY and Y = C + S we get S = Y − C = −a + (1 − b)Y = −a + MPS·Y. Note the negative intercept (−a) when Y = 0.

Investment (I): Expenditure on capital goods. In the simple Keynesian model, investment is often treated as autonomous (independent of current income). Distinguish:

• Autonomous investment: fixed by firms’ plans (e.g., a firm builds a new factory).
• Planned/desired investment vs actual investment: Actual investment = planned investment + unplanned changes in inventories. Unplanned inventory changes arise when actual sales differ from expected sales.

Deficiency of Effective Demand: When planned AD < full‑employment output; firms reduce production and lay off workers, causing unemployment.

Excess Demand: When AD > current output, leading firms to increase production and employment (until capacity is reached).

Multiplier: The process by which an autonomous change in spending (typically investment) induces a larger change in equilibrium income. For the linear consumption function, the simple (income‑expenditure) multiplier is k = 1 / (1 − MPC) = 1 / MPS. The equilibrium income change is ΔY = k · ΔI.

Equilibrium Level of Income (Y*): Level of output where planned aggregate demand equals aggregate supply (or planned expenditure equals output). Using C = a + bY and constant autonomous investment I, equilibrium is given by:

Y* = (a + I) / (1 − b)

Full Employment Equilibrium: A situation where equilibrium Y* equals the full‑employment level of output. If Y* < full employment, the economy faces involuntary unemployment (deficient demand).