An economy has a fixed price level, no imports, and no income taxes. An increase in autonomous expenditure of $2 trillion increases equilibrium expenditure by $8 trillion

Calculate the multiplier and explain what happens to the multiplier if an income tax is introduced.

The multiplier is defined as the change in equilibrium expenditure divided by the change in autonomous expenditure. In this problem the multiplier equals $8 trillion ÷ $2 trillion which is 4.0
If an income tax is introduced, the multiplier decreases in value. With an income tax, at each spending round less disposable income is created leading to smaller increases in induced expenditure.