Multiplier and Accelerator

1) Multiplier: recap and meaning

The multiplier shows how a change in autonomous spending causes a larger change in equilibrium income.

In the simple 2-sector Keynesian model:

and:

where $\Delta A$ is a change in autonomous expenditure (like investment).

Intuition: spending generates income → part of income is spent again → rounds of spending continue.

2) Leakages and multiplier size

Multiplier is smaller when leakages are larger:

• saving (MPS),
• taxes,
• imports.

General idea: more leakages → weaker multiplier.

3) Accelerator: meaning

The accelerator principle links induced investment to changes in output/income.

Key idea:

• Firms invest more when output is rising, to expand capacity.
• Investment depends on the rate of change of output, not the level.