Determination of Income and Employment

AGGREGATE DEMAND AND ITS COMPONENTS

**Aggregate Demand (AD)** is the total planned expenditure on final goods and services in an economy at different income levels. It comprises two main components: **Consumption (C)** and **Investment (I)** in a two-sector model. In a three-sector model, government expenditure (G) is added.

Ex-Ante and Ex-Post Values

**Ex-ante** refers to **planned or intended values** — what households and firms plan to consume, invest, or produce

**Ex-post** refers to **actual or realized values** — what actually happens during a given period

**Example:** A producer plans to add Rs 100 to inventory (planned/ex-ante investment = Rs 100). Due to unexpected demand surge, she sells Rs 30 from stock, so actual inventory increase = Rs 70 (ex-post investment = Rs 70). The difference is explained by **unplanned inventory investment = −Rs 30**.

This distinction is **crucial** because equilibrium occurs when **ex-ante (planned) aggregate demand = ex-ante (planned) aggregate supply**. The accounting identity (ex-post equality) always holds because unplanned inventory changes adjust to make it true.

CONSUMPTION FUNCTION AND RELATED CONCEPTS

**Consumption Function** describes the relationship between consumption expenditure and income. The **linear consumption function** is:

**C = C̄ + cY**

Where:

**C** = total consumption expenditure

**C̄** (C-bar) = **autonomous consumption** — consumption when income = 0 (subsistence level; depends on previous wealth, habits, expectations)

**c** = **Marginal Propensity to Consume (MPC)** — slope of consumption function

**Y** = disposable income (in a two-sector model without government)

Autonomous Consumption (C̄)

Independent of current income

Represents minimum consumption needed for survival

Can be financed through past savings or borrowing

**Example:** Even in year of zero income, person consumes Rs 500 from savings (C̄ = 500)

Induced Consumption (cY)

Depends directly on income

Component that varies with income changes

As income rises by Re 1, consumption rises by **c** rupees

**Example (Imagenia):** C = 100 + 0.8Y

Autonomous consumption = Rs 100 (consumed even at zero income)

MPC = 0.8 (if income increases by Rs 100, consumption increases by Rs 80)

Marginal Propensity to Consume (MPC)

**MPC = c = ΔC/ΔY** (change in consumption per unit change in income)

**Range:** 0 ≤ MPC ≤ 1

**MPC = 0:** increase in income not spent on consumption (entire increase saved)

**MPC = 1:** entire income increase spent on consumption (no savings)

**0 < MPC < 1:** income increase partially consumed, partially saved (most realistic)

**Exam Note:** MPC reflects consumer behavior — as income rises, people increase consumption but not by full amount of increase.

Savings Function

**Savings (S)** = Income not consumed = Y − C

**S = −C̄ + (1 − c)Y**

Or: **S = −C̄ + sY**

Where **s = MPS (Marginal Propensity to Save)**

Marginal Propensity to Save (MPS)

**MPS = s = ΔS/ΔY** (change in savings per unit change in income)

**Fundamental Identity:** **MPC + MPS = 1** (or c + s = 1)

This means: every rupee of additional income is either consumed or saved; no other use possible.

**Example:** If MPC = 0.8, then MPS = 0.2 (out of Re 1 additional income, 80 paise consumed, 20 paise saved)

Average Propensity to Consume and Save

**APC (Average Propensity to Consume) = C/Y** — fraction of total income consumed

**APS (Average Propensity to Save) = S/Y** — fraction of total income saved

**APC + APS = 1** (similarly)

**Important distinction:** MPC (marginal) ≠ APC (average). As income rises, APC typically falls while MPC remains constant.

INVESTMENT FUNCTION

**Investment** is defined as **addition to stock of physical capital** (machines, buildings, roads, factories) and **changes in inventory** (stock of finished goods).

**Key Points:**

Investment goods are **final goods** (not intermediate goods like raw materials)

Machines produce output over multiple years, not consumed in one period

Includes both **gross fixed capital formation** and **inventory investment**

Investment as Autonomous Expenditure

For simplicity, investment is assumed **autonomous (exogenous)**:

**I = Ī** (constant, independent of income level)

**Graphically:** horizontal line at height Ī above horizontal axis

Factors Affecting Investment (in reality)

**Interest rate:** Higher interest rates increase cost of borrowing; firms reduce investment

**Availability of credit:** Easy credit expansion encourages investment

**Expected profit:** Higher business confidence → higher investment

**Technology:** Newer technology adoption prompts capital expenditure

**Exam Context:** While chapter assumes I is autonomous for analytical simplicity, understanding actual determinants is important for policy discussions.

DETERMINATION OF INCOME IN TWO-SECTOR MODEL

In an economy with only **households (consumers) and firms (producers)**, without government:

**Aggregate Demand: AD = C + I**

Substituting consumption and investment functions:

**AD = C̄ + cY + Ī**

Or: **AD = Ā + cY**

Where **Ā = C̄ + Ī** = **total autonomous expenditure**

Equilibrium Condition

**Equilibrium occurs when: Planned Output (Y) = Planned Aggregate Demand (AD)**

**Y = Ā + cY**

Solving for equilibrium income (Y*):

**Y − cY = Ā**

**Y(1 − c) = Ā**

**Y* = Ā/(1 − c)** or **Y* = Ā/s** or **Y* = Ā × k**

Where **k = 1/(1 − c) = 1/s = multiplier**

Inventory Investment and Equilibrium Adjustment

If **Planned Y > AD:** firms produce more than consumers/investors demand. Excess output accumulates as **unplanned positive inventory investment**. This signals disequilibrium; firms reduce production.

If **Planned Y < AD:** demand exceeds planned output. Firms experience **unplanned negative inventory investment** (stockouts). They increase production.

**Only when AD = Y does unplanned inventory investment = 0, confirming equilibrium.**

Example Calculation

Given: C = 100 + 0.8Y, Ī = 50

Equilibrium: Y = 100 + 0.8Y + 50

Y − 0.8Y = 150

0.2Y = 150

**Y* = 750**

Or using multiplier: k = 1/0.2 = 5, so Y = 5 × (100 + 50) = 5 × 150 = 750

INCLUSION OF GOVERNMENT

When government is introduced into the economy:

**Government expenditure (G)** adds to aggregate demand (like consumption and investment)

**Taxes (T)** reduce household disposable income

**Disposable Income (Yd) = Y − T**

Households consume fraction c of disposable income, not total income

**Modified equilibrium equation:**

**Y = C̄ + Ī + G + c(Y − T)**

**Government components (G and cT) form part of autonomous expenditure**, shifting AD function but not changing slope (MPC remains c).

**For analytical simplicity in this chapter, government sector is largely ignored**, focusing on two-sector determination first.

MACROECONOMIC EQUILIBRIUM WITH FIXED PRICE LEVEL

Justification for Fixed Price Assumption

**Why assume price level constant?**

1. **Unused resources exist:** economy has unemployment of labor, idle capacity of machinery. Law of diminishing returns doesn't apply; additional output produced without increasing marginal cost, so **prices unchanged**

2. **Analytical simplification:** focuses analysis on quantity/income determination separately; price level adjustment introduced later

Graphical Analysis

**Consumption Function (C = C̄ + cY):**

**Vertical intercept** = C̄ (consumption at Y = 0)

**Slope** = c (angle tan α = c = MPC)

Upward sloping, linear relationship

**Investment Function (I = Ī):**

**Horizontal line** at height Ī

Shows investment independent of income level

Perfectly inelastic to income changes

**Aggregate Demand Function (AD = C̄ + Ī + cY):**

Obtained by **vertically adding** C and I curves

**Vertical intercept** = C̄ + Ī

**Slope** = c (same as consumption function)

Parallel to consumption function

**Aggregate Supply (45° line):**

Every point on this line has equal horizontal and vertical coordinates

If GDP = Rs 1000, aggregate supply = Rs 1000

Shows that at fixed prices, whatever output planned will be supplied

Represents economy's willingness to produce

Equilibrium Point

**Graphically:** intersection of AD curve and 45° line

At equilibrium point:

**Ex-ante AD = Ex-ante AS**

**No unplanned inventory investment**

**No pressure on firms to change production**

**Exam Focus:** Understanding why 45° line represents supply (not traditional upward-sloping curve) and how equilibrium is determined visually is essential.

EFFECT OF AUTONOMOUS CHANGES IN AGGREGATE DEMAND

Sources of AD Changes

1. **Change in autonomous consumption (C̄):** due to shifts in consumer preferences, wealth, or expectations

2. **Change in MPC (c):** behavioral change in consumption pattern (less likely to vary)

3. **Change in investment (Ī):** due to interest rate changes, credit availability, technology improvements, business confidence

Multiplier Effect — Income Changes by More than Initial AD Change

**Numerical Example:**

Initial: C = 40 + 0.8Y, Ī = 10

Equilibrium: Y = 40 + 10 + 0.8Y → 0.2Y = 50 → **Y₁ = 250**

Investment rises: Ī = 20 (increase of 10)

New equilibrium: Y = 40 + 20 + 0.8Y → 0.2Y = 60 → **Y₂ = 300**

Income increase = 300 − 250 = **50** (not just 10)

**Multiplier k = ΔY/ΔĪ = 50/10 = 5** (also = 1/0.2 = 1/MPS)

Why Multiplier Effect Occurs

When autonomous expenditure (say investment) increases by ΔĪ:

1. **Direct effect:** demand increases by ΔĪ

2. **Indirect effect:** higher income leads to increased consumption (cΔĪ), which generates further income

3. **Chain reaction:** this additional consumption income generates more consumption (c²ΔĪ), and so on

4. **Total effect:** ΔY = ΔĪ(1 + c + c² + c³ + ...) = ΔĪ × [1/(1−c)] = ΔĪ × k

**Multiplier (k) = 1/(1−c) = 1/MPS**

Since 0 < c < 1:

**Higher MPC → larger multiplier** (more consumption, more income generation)

**Lower MPS → larger multiplier** (less savings leakage)

**Minimum k = 1** (when c = 0, MPS = 1, entire increase saved)

**Maximum k = ∞** (theoretically, when c = 1, MPS = 0, no savings limit)

Graphical Representation of Shift

When investment increases from Ī to Ī₂:

**AD curve shifts upward vertically by (Ī₂ − Ī)** — parallel shift (slope unchanged)

**New intersection with 45° line** at higher income level

**Income increase exceeds initial expenditure increase** due to multiplier

Deflationary Gap

**Deflationary gap** = situation where **actual AD < full employment AD**

Economy operates **below potential output**

Unemployment exists, excess capacity in firms

**Solution:** government can increase G or reduce T to shift AD rightward until full employment level reached

Inflationary Gap

**Inflationary gap** = situation where **actual AD > full employment AD**

Demand exceeds economy's productive capacity

Upward pressure on prices (though chapter assumes fixed prices)

**Solution:** government can reduce G or increase T to shift AD leftward to full employment level

**Exam Importance:** Understanding deflationary/inflationary gaps is critical for policy recommendations questions.

CRITICAL DISTINCTIONS FOR BOARD EXAM

**Planned vs Actual Investment:**

Planned investment = what firms intend

Actual = planned + unplanned (inventory changes)

Only planned values used in equilibrium equation

**MPC vs APC:**

MPC = slope of consumption function (constant for linear function)

APC = C/Y (changes as income level changes)

MPC relevant for multiplier calculation

**Autonomous vs Induced Expenditure:**

Autonomous = independent of income (C̄, Ī, G in three-sector)

Induced = depends on income (cY)

Shifts in autonomous affect equilibrium directly; shifts in MPC affect multiplier

**Ex-ante vs Ex-post:**

Used throughout macro analysis

Equilibrium requires ex-ante equality

Accounting identity shows ex-post always equal (with inventory adjustment)