Explanation of Dynamic Multiplier

The government (or firms) makes a one-time increase in investment of ΔI. After this single injection, no further new investment is added. How does income unfold over time?

Case 1: MPC = 0 → Multiplier = 1

What this means: Nobody spends any extra income — they save it all. The multiplier = 1/(1−0) = 1.

When MPC = 0, the multiplier is at its minimum value of 1. Total income increase = Initial investment. No ripple effect occurs.

Case 2: MPC = ½ → Multiplier = 2

\[\begin{array}
{c}\mathrm{K}=\frac{1}{1-c}=\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=2
\end{array}\]
What this means: People spend half of every extra rupee and save the other half. K = 1/(1−0.5) = 2.

Real-Life Parallel
The government spends ₹100 crore building a highway. Workers earn ₹100 crore and spend ₹50 crore on food, clothes, transport. Shopkeepers now earn ₹50 crore extra and spend ₹25 crore. The chain continues — each round being half the previous one.

Case 3: MPC = 1 → Multiplier = ∞

\[\mathrm{K}=\frac{1}{1-c}=\frac{1}{1-1}=\frac{1}{0}=\infty\]
What this means: Every rupee of extra income is spent — nobody saves anything. K = 1/(1−1) = ∞. This is a theoretical extreme.

In reality, investment is not a one-time event. Governments announce capital expenditure budgets every year. The repeated-dose scenario assumes that the same amount of new investment (ΔI) is injected every period.

Case 1: MPC = 0 → Multiplier = 1 (Repeated)

\[\mathrm{K}=\frac{1}{1-c}=\frac{1}{1-0}=\frac{1}{1}=1\]
Fresh investment of ₹100 crore arrives every period. Since MPC = 0, nobody spends the extra income — no ripple effects. Each period's income increase comes solely from that period's investment.

Case 2: MPC = ½ → Multiplier = 2 (Repeated) — Most Realistic

\[\mathrm{K}=\frac{1}{1-c}=\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=\frac{2}{1}=2\]
This is the most instructive case. Each period adds fresh investment plus induced consumption from previous periods.

Repeated investment with MPC = ½ creates a steadily rising income stream that eventually stabilises at K × ΔI = 200 crore per period. The full multiplier effect takes several periods to materialise.

Case 3: MPC = 1 → Multiplier = ∞ (Repeated)

\[\mathrm{K}=\frac{1}{1-c}=\frac{1}{1-1}=\frac{1}{0}=\infty\]
Fresh investment arrives every period and nobody saves. Income grows without limit — each period's income = new investment + entire previous income spent as consumption.

Repeated doses with MPC = 1 lead to explosive, unlimited income growth. This is purely theoretical — it underscores why even small amounts of saving (MPC < 1) are crucial for the economy to reach a stable equilibrium.

• Dynamic multiplier shows how income increases over time with time lags, not instantly.
• Income rises in successive periods as consumption depends on past income.
• With a single investment, income expansion stops unless MPC = 1.
• With repeated investment, income rises gradually and finally stabilises (or becomes infinite if MPC = 1).