Balancing the budget

Step 1 The tax increase

The additional £30m taken in tax reduces disposable income by £30m, but £6m of that £30m would have been saved had households still received it (assuming a marginal propensity to consume of 0.8), so the initial fall in aggregate demand resulting from the tax increase is only £24m. The increase in the tax rate from 0.05 to 0.1 reduces the multiplier, as you know from the earlier example, from 4.17 to 3.57. Applying the multiplier of 3.57 to the £24m fall in spending gives a fall in income due to the tax increase of 3.57 × £24m = £85.7m.

Step 2 The increase in government spending

The increase in government spending gives an initial boost of £30m to aggregate demand. Again applying the multiplier shows that there is an increase in income of 3.57 × £30m = £107.1m.

Step 3 The net effect

You have seen that the tax increase alone would reduce income by £85.7m but that the increase in government spending would increase income by £107.1m. To calculate the net effect of these tax and spending changes, I need to subtract 85.7 from 107.1. I conclude that income increases by £107.1m − £85.7m = £21.4m to a new equilibrium level of £621.4m.

So even though the increase in government spending has been backed by a tax increase, the overall impact is expansionary. The government can effectively gather what households would have saved as tax revenue and spend it. It may even be possible to spend your way out of a crisis and balance the budget.

A problem, however, for policymakers, is that a balanced budget expansion may not be very expansive. In the example above, £30 million extra in government spending produced a £21.4 million increase in income, so it could be said that the balanced-budget multiplier was 21.4/30 = 0.71. The increase in spending, once it has been covered by a tax increase, may be too small to make much of a difference. There is also, therefore, a Keynesian case for increasing the size of the deficit in times of recession.