Why, when the price level is fixed, will a change in government expenditures or the rate of income tax have a multiplier effect on real GDP. Explain why the multiplier effect of a change in government expenditures is greater than an equivalent change in taxation.
The multiplier denotes the numerical effect of any change in aggregate demand on the final level of real income. Hence, numerically, it is calculated by dividing the final increase in real income by the initial increase in aggregate demand (spending).
Any increase in any of the component parts of aggregate demand represents an injection into the circular flow of income. Hence, for example, if there is an increase in government spending on housebuilding, this provides new income to the firms, suppliers and workers in the industry equal to the government's expenditure. They will then in turn spend some proportion of this income, while the remainder is saved, taken in taxation or leaked out of the economy through purchase of imports. The proportion of the new income spent is given by the value of the marginal propensity to consume. If, for example, this is 0.8, then it means that four fifths of the income is spent and thus passed on in the circular flow, creating new income for the producers and workers in those industries whose goods and services are now newly consumed. They in turn will spend four-fifths of their additional income, creating in turn nnew income for another group of producers and workers. This multiplier process continues indefinitely in successive rounds of spending and income generation. Hence, for example, if the initial injection were £100 million and the value of the marginal propensity to consume were 0.8, then the value of the multiplier is given by the formula: 1 divided by (1 minus mpc) - so in this case, we have 1 divided by (1 minus 0.8) and so the value of the multiplier is 5. Hence the initial increase in government spending will create a final increase in income of £500 million. Similarly, a reduction in the rate of income tax would leave consumers with higher disposable income. They will therefore spend more - an injection into the economy, and setting off a multiplier effect.
Your second question refers to the Balanced Budget Multiplier. Suppose the mpc is 0.8. Suppose the government increases its spending by £100 million and finances it by raising taxes by £100 million. In this case the multiplier is 5. So the increase in government spending will lead to a final increase in income of £100M x 5 - i.e. £500M. Now look at the increase in taxation of £100M. Since the mpc is 0.8, only £80M of this comes from reduced consumption. The remaining £20M comes from reduced saving and spending on imports. Hence only the fall in consumption of £80M is subject to a (downward) multiplier effect. Since the multiplier here is 5, the final fall in income will be £80M x 5 - i.e. £400M.
So we get the Balanced Budget Multiplier Theorem. A tax-financed increase in government spending will raise income by the same amount. In the above example, the rise in government spending raises income by £500M. The rise in tax lowers income by £400M. Hence the net effect is to increase income by £100M. The outcome will be the same regardless of the value of the mpc.
I hope this is helpful.