Keynesian Multiplier & Aggregate Demand: Complete Notes with 10+ Solved Numerical Problems

Introduction to the Keynesian Model

The Keynesian theory of income and employment determination revolutionized macroeconomic thought. At its core is the principle of effective demand: equilibrium income is determined where Aggregate Demand (AD) equals Aggregate Supply (AS). In this post, we cover the multiplier effect, various sector models, and provide extensive solved numericals.

Two-Sector Keynesian Model (C + I)

In a simple two-sector economy, Aggregate Demand consists of Consumption (C) and Investment (I).

The Consumption Function

C = a + bY

Where 'a' is autonomous consumption (consumption when income is zero), 'b' is the Marginal Propensity to Consume (MPC), and 'Y' is income.

APC vs MPC: Average Propensity to Consume (APC) is C/Y. Marginal Propensity to Consume (MPC) is the change in C divided by the change in Y.

Investment Multiplier Derivation

The investment multiplier (k) measures how much equilibrium income changes for a given change in autonomous investment.

Y = C + I

Y = a + bY + I

Y - bY = a + I

Y(1 - b) = a + I

Y = (a + I) / (1 - b)

Change in Y = Change in I / (1 - b). Thus, Multiplier k = 1 / (1 - MPC).

Three-Sector Model (Adding Government)

When we introduce the government, AD = C + I + G. Income Y = C + I + G.

Taxes (T) reduce disposable income (Yd = Y - T). Consumption becomes C = a + b(Y - T).

Tax Multiplier and Balanced Budget Multiplier

Tax Multiplier = -b / (1 - b)

Government Expenditure Multiplier = 1 / (1 - b)

Balanced Budget Multiplier: When change in G = change in T, the multiplier is exactly 1. This means an equal increase in government spending and taxes increases income by exactly that amount.

Four-Sector Model (Adding Trade)

AD = C + I + G + (X - M), where X is exports and M is imports. Imports often depend on income: M = mY, where 'm' is the marginal propensity to import.

Foreign Trade Multiplier = 1 / (1 - b + m).

Key Concepts: Paradox of Thrift and Gaps

Paradox of Thrift

If everyone in an economy tries to save more, aggregate demand falls, leading to a drop in total output and income. Ultimately, total savings may remain unchanged or even fall. What is good for an individual (saving) can be detrimental to the economy as a whole.

Inflationary & Deflationary Gaps

Deflationary Gap: The shortfall in aggregate demand relative to the full-employment level of output. It leads to unemployment.

Inflationary Gap: The excess of aggregate demand over the full-employment level of output. It leads to demand-pull inflation.

10+ Solved Numerical Problems

Problem 1: Simple Multiplier

If MPC = 0.8 and Investment increases by 100, find the change in Income.

Solution: Multiplier k = 1 / (1 - 0.8) = 1 / 0.2 = 5.

Change in Income = k * Change in I = 5 * 100 = 500.

Problem 2: Finding Equilibrium Income

C = 50 + 0.75Y, I = 100. Find equilibrium Y.

Solution: Y = C + I

Y = 50 + 0.75Y + 100

Y - 0.75Y = 150

0.25Y = 150

Y = 600.

Problem 3: Three-Sector Equilibrium

C = 100 + 0.8Yd, I = 50, G = 50, T = 40. Find Y.

Solution: Yd = Y - 40

Y = C + I + G = 100 + 0.8(Y - 40) + 50 + 50

Y = 200 + 0.8Y - 32

Y = 168 + 0.8Y

0.2Y = 168

Y = 840.

Diagrammatic Explanations

The Keynesian Cross diagram illustrates the equilibrium where the AD curve (C+I+G+NX) intersects the 45-degree line (where Y = AD). Shifts in the AD curve, such as an increase in G, result in a larger shift in equilibrium Y, demonstrating the multiplier effect visually.