Changes in Taxes

• Disposable Income - Income remaining with households after paying taxes: \[Y_D = Y - T\]
• Marginal Propensity to Consume (c) - The fraction of additional income that a household spends on consumption.
• Automatic Stabiliser - A fiscal mechanism (like proportional taxes or transfers) that automatically reduces fluctuations in GDP without any new policy action.

• A cut in taxes ↑ disposable income (\[Y - T\])
• Higher disposable income ↑ consumption, which ↑ aggregate expenditure.
• The aggregate expenditure curve shifts upward by \[c \times \Delta T\].
• Result: National income (output) increases.

Effect of Higher Government Expenditure

\[\frac{\Delta Y}{\Delta T} = \frac{-c}{1-c}\]

\[\frac{\Delta Y}{\Delta G} = \frac{1}{1-c}\]

\[\frac{\Delta Y}{\Delta G} = 1 \quad \text{when } \Delta G = \Delta T\]

\[\frac{\Delta Y}{\Delta TR} = \frac{c}{1-c}\]

• \[\Delta Y\] = Change in national income
• \[\Delta T\] = Change in taxes
• \[\Delta G\] = Change in government expenditure
• \[\Delta TR\] = Change in transfer payments
• \[c\] = Marginal propensity to consume

• When the government increases both spending and taxes by the same amount (\(\Delta G = \Delta T\)), the net effect on income is still positive.
• The balanced budget multiplier = 1.
• Income rises by exactly the amount of the increase in government spending.

• Fixed tax: (T) (lump sum)
• Proportional tax: (T = tY), where (t) = tax rate.
• Disposable income becomes: \[(1-t)Y\]

Effect on the economy:

Government and Aggregate Demand (proportional taxes make the AD schedule flatter)

• Makes the AD (Aggregate Demand) schedule flatter.
• Reduces the value of the multiplier.
• Acts as an automatic stabiliser.

• Proportional income taxes and transfers automatically reduce economic fluctuations.
• During a boom: GDP ↑ → tax collection ↑ → disposable income rises by less → consumption spending is dampened.
• During a recession: GDP ↓ → taxes ↓ → disposable income is cushioned → fall in consumption is reduced.
• No new policy needed — the system corrects itself.

Increase in Government Expenditure (with proportional taxes)

• Government transfers raise household income, but only a fraction \(c\) is spent.
• Transfer multiplier \(\frac{c}{1-c}\) is smaller than the government expenditure multiplier \(\frac{1}{1-c}\).
• Reason: Direct govt. spending adds fully to demand; transfers add only the consumed portion.

Given: Marginal Propensity to Consume (c = 0.8)

Observation: The tax multiplier (–4) is smaller in magnitude than the govt. expenditure multiplier (5).

Given: Marginal Propensity to Consume (c = 0.8), tax rate (t = 0.25)

\[c(1-t) = 0.8(1-0.25) = 0.8 \times 0.75 = 0.60\]

Government expenditure multiplier with proportional taxes:

\[\frac{1}{1-c(1-t)} = \frac{1}{1-0.60} = \frac{1}{0.40} = 2.5\]

If government expenditure rises by 100, output rises by:

\[2.5 \times 100 = 250\]

This is smaller than the increase in output with lump-sum taxes.

Given: Marginal Propensity to Consume (c = 0.75)

When government purchases increase by 20:

\[\Delta Y = \frac{1}{1-0.75}\Delta G = 4 \times 20 = 80\]

When transfers increase by 20:

\[\Delta Y = \frac{0.75}{1-0.75}\Delta TR = 3 \times 20 = 60\]

Thus, income increases by less than it increased with a rise in government purchases.

• A tax cut raises disposable income and shifts aggregate expenditure up by \(c \times \Delta T\), increasing output.
• The tax multiplier is negative and smaller in absolute value than the govt. expenditure multiplier.
• The balanced budget multiplier = 1 - equal increases in G and T still raise income.
• Proportional taxes flatten the AD curve and lower the multiplier value.
• Proportional taxes and transfers act as automatic stabilisers - they cushion GDP swings without new policy action.
• The transfer multiplier is positive but smaller than the expenditure multiplier, as only a fraction of transfers is spent.