Dynamic Concept of Multiplier

The dynamic multiplier is a more realistic version of Keynes' investment multiplier, developed by economists like Hicks, Hansen, Samuelson, Harris, and Kurihara. Unlike the static (Keynesian) multiplier — which assumes income changes instantly and completely the moment investment changes — the dynamic multiplier accounts for time lags in the income generation process.

Assumption 1 — Consumption Depends on the Previous Period's Income

\[C_t=f(Y_{t-1})\]

What you earn in April determines what you spend in May. There is a one-period consumption lag — people adjust their spending based on the income they received in the previous period, not the current one.

Assumption 2 — Lagged Adjustment Between Investment and Income

\[Y_{t+1}=f(I_t)\]

Investment in one period does not generate income in the same period. The income effect appears in the next period. If the government invests ₹100 crores in Period 1, construction workers and suppliers receive that income in Period 2.​

Assumption 3 — Current Expenditure Determines Next Period's Income

\[E_t\Rightarrow Y_{t+1}\]

Whatever is spent in the economy during Period 1 becomes someone's income in Period 2. Changes in income in the next period are exactly equal to changes in expenditure in the current period.

Starting from Assumption 3:​

Step 1: Current expenditure equals next period's income:

\[E_t=Y_{t+1}\]

Step 2: Subtract YtYt from both sides:

\[E_t-Y_t=Y_{t+1}-Y_t\]
\[E_t-Y_t=\Delta Y_{t+1}\]

Step 3: Since today's income equals yesterday's expenditure (Yt=Et−1Yt=Et−1):

\[E_t-E_{t-1}=\Delta Y_{t+1}\]

Step 4: Therefore:

\[\Delta E_t=\Delta Y_{t+1}\]

Conclusion: The change in expenditure in the current period equals the change in income in the next period. This is the fundamental time-lag equation of the dynamic multiplier.

• The dynamic multiplier considers the time lag between changes in investment and changes in income.
• Income adjustment takes place over successive periods, not instantly as in the static multiplier.
• Consumption depends on past income, and investment in one period affects income in the next period.
• Since MPC changes over time, the multiplier process becomes dynamic and more realistic.