Determination of Income & Employment – Study Guide (Chapter 4)
1. Aggregate Demand and Its Components
Aggregate demand (AD) is the total planned expenditure on final goods and services in an economy at a given price level and time period. In a simple closed economy without government and foreign trade, aggregate demand equals C + I, where:
- C = Consumption expenditure by households
- I = Investment expenditure by firms (gross investment)
In the presence of government and external sector, AD expands to C + I + G + (X − M).
AD = C + I
Aggregate demand is often drawn as a downward-sloping curve in price–output space; here, for short-run income determination, we treat price level as fixed (Keynesian short run).
2. Consumption
Consumption (C) is the total spending by households on goods and services. Keynesian consumption theory distinguishes between autonomous consumption (consumption that occurs even at zero income) and induced consumption (consumption that varies with income).
C = C₀ + cYdWhere:
- C₀ = Autonomous consumption (independent of income)
- c = Marginal propensity to consume (MPC): fraction of an additional rupee of disposable income spent on consumption
- Yd = Disposable income (here, in a simple model, Yd=Y)
| Concept | Definition |
|---|---|
| MPC (c) | ΔC / ΔY — how much consumption changes when income changes by one unit |
| APS (average propensity to save) | S/Y = 1 − (C/Y) |
| MPS | Marginal propensity to save = 1 − c |
3. Investment
Investment (I) refers to spending on capital goods — new factories, machinery, inventories, etc. In the Keynesian short-run model, investment is treated as autonomous (I₀) — determined by business expectations and interest rates.
Investment decisions depend on the expected rate of return on capital and the market interest rate. In simple exercises we take I = I₀, i.e., independent of current income.
4. Determination of Income in a Two-Sector Model (No Government, No Foreign)
In a two-sector closed economy (Households + Firms):
AD = C + IEquilibrium national income (Y*) is where aggregate demand equals aggregate output (or aggregate supply):
Y = AD = C + ISubstitute consumption function:
Y = C₀ + cY + I₀Solve for equilibrium income Y:
Y − cY = C₀ + I₀ → Y(1 − c) = C₀ + I₀ Y* = (C₀ + I₀) / (1 − c)This gives the equilibrium income as a function of autonomous spending and MPC.
Suppose C₀ = 500, I₀ = 1500, c = 0.75. Then Y* = (500 + 1500) / (1 − 0.75) = 2000 / 0.25 = ₹8000.
5. Determination of Equilibrium in the Short Run (Price Level Fixed)
Key assumptions (Keynesian short run):
- Price level is fixed (no price adjustments).
- Output adjusts to ensure planned expenditure equals production.
- Wages and prices sticky → firms meet demand by changing output and employment.
Graphically, equilibrium is found at the intersection of the Aggregate Expenditure (AE) line and the 45° line (where Y = AE). The slope of AE (in closed 2-sector) = MPC (c).
45° line: all points where production = income.
AE line: AE = C₀ + cY + I₀ (upward sloping).
Intersection → equilibrium Y*.
6. Effect of an Autonomous Change in Aggregate Demand on Income and Output
An autonomous change (ΔA) in aggregate demand — such as a change in I₀ or C₀ or G — shifts the AE line up or down. The resulting change in equilibrium income is amplified by the multiplier.
ΔY = k × ΔAWhere k is the multiplier:
k = 1 / (1 − c) = 1 / MPSMultiplier amplification works because initial additional spending becomes income for others, who then spend part of it, creating further income.
7. The Multiplier Mechanism (Step-by-Step)
Mechanics of the multiplier:
- Stage 0: Autonomous increase in demand (ΔA) occurs — e.g., investment rises.
- Stage 1: Producers increase output by ΔA and pay incomes to households.
- Stage 2: Households consume fraction c of the new income and save (1−c).
- Stage 3: The consumed portion becomes income for other producers → induces further consumption.
- This process continues until induced spending becomes negligible; total ΔY = ΔA × k.
8. Paradox of Thrift
The Paradox of Thrift states that when households collectively try to increase saving (reduce consumption) during a downturn, aggregate demand falls, output and income decline, and total saving in the economy may actually fall — the attempt to save more is self-defeating.
The paradox highlights when individual rational behaviour (save more) aggregates to a collectively undesirable outcome (lower income).
9. Worked Problems & Practice Questions
Y = C + I = 200 + 0.75Y + 800 → Y − 0.75Y = 1000 → 0.25Y = 1000 → Y = 4000.
Consumption C = 200 + 0.75×4000 = 200 + 3000 = 3200.
Saving S = Y − C = 4000 − 3200 = ₹800.
Try additional practice: change MPC, introduce taxes (see below), or include government to see fiscal policy effects.
10. Extensions & Short Notes
a) Introducing Government (Three-Sector Model)
With government, aggregate demand becomes AD = C + I + G. If taxes (T) exist and disposable income = Y − T, consumption becomes C = C₀ + c(Y − T). The equilibrium income changes accordingly:
Y = C₀ + c(Y − T) + I₀ + G → Y(1 − c) = C₀ − cT + I₀ + Gb) Introducing Taxes & Autonomous Changes
With lump-sum taxes T, the multiplier falls because part of income is withdrawn. The tax-adjusted multiplier is:
k = 1 / (1 − c(1 − t))Where t is proportional tax rate (if applied), otherwise with lump-sum taxes use reduced form above.
c) Role of Expectations & Interest Rate
Investment is sensitive to expectations and firm borrowing costs. A fall in interest rates raises planned investment and shifts AD upward; similarly, positive business expectations raise I₀.
11. Summary Table – Key Equations & Concepts
| Item | Equation / Definition |
|---|---|
| Consumption function | C = C₀ + cY |
| Equilibrium income (2-sector) | Y* = (C₀ + I₀) / (1 − c) |
| Multiplier | k = 1 / (1 − c) |
| Change in income | ΔY = k × ΔA |
| Paradox of thrift | Higher aggregate saving desire can reduce total income & actual saving |
12. Quick Revision Checklist
- Be able to derive Y* from the consumption function and autonomous spending.
- Understand and compute the multiplier for different MPC values.
- Explain the 45° diagram equilibrium (graphical method).
- Apply the model to simple numerical problems (find Y, C, S given parameters).
- Know how taxes, government spending and net exports alter the equilibrium.
- Discuss the Paradox of Thrift in words with numeric intuition.
13. Concluding Insights
The Keynesian short-run framework shows how aggregate demand determines output and employment when prices are sticky. Autonomous changes in spending are magnified via the multiplier, so fiscal policy (G and T) can be powerful in stabilizing the economy. However, real-world complexities — expectations, interest rates, openness, supply constraints and price adjustments — require careful extension of the simple model when applying it to policy problems.