Assume inflation is stable, there is excess productive capacity, and the central bank maintains its current monetary policy setting. If government spending increases by $X dollars and private investment and exports are unchanged, then nominal income will continue growing until the sum of the change in taxation revenue, import spending and household saving rises by $X dollars.
Answer: True
The answer is True.
This question relates to the concept of a spending multiplier and the relationship between spending injections and spending leakages.
We have made the question easy by assuming that only government spending changes (exogenously) in period one and then remains unchanged after that.
Aggregate demand drives output which then generates incomes (via payments to the productive inputs). Accordingly, what is spent will generate income in that period which is available for use. The uses are further consumption; paying taxes and/or buying imports.
We consider imports as a separate category (even though they reflect consumption, investment and government spending decisions) because they constitute spending which does not recycle back into the production process. They are thus considered to be "leakages" from the expenditure system.
So if for every dollar produced and paid out as income, if the economy imports around 20 cents in the dollar, then only 80 cents is available within the system for spending in subsequent periods excluding taxation considerations.
However there are two other "leakages" which arise from domestic sources - saving and taxation. Take taxation first. When income is produced, the households end up with less than they are paid out in gross terms because the government levies a tax. So the income concept available for subsequent spending is called disposable income (Yd).
To keep it simple, imagine a proportional tax of 20 cents in the dollar is levied, so if $100 of income is generated, $20 goes to taxation and Yd is $80 (what is left). So taxation (T) is a "leakage" from the expenditure system in the same way as imports are.
Finally consider saving. Consumers make decisions to spend a proportion of their disposable income. The amount of each dollar they spent at the margin (that is, how much of every extra dollar to they consume) is called the marginal propensity to consume. If that is 0.80 then they spent 80 cents in every dollar of disposable income.
So if total disposable income is $80 (after taxation of 20 cents in the dollar is collected) then consumption (C) will be 0.80 times $80 which is $64 and saving will be the residual - $26. Saving (S) is also a "leakage" from the expenditure system.
It is easy to see that for every $100 produced, the income that is generated and distributed results in $64 in consumption and $36 in leakages which do not cycle back into spending.
For income to remain at $100 in the next period the $36 has to be made up by what economists call "injections" which in these sorts of models comprise the sum of investment (I), government spending (G) and exports (X). The injections are seen as coming from "outside" the output-income generating process (they are called exogenous or autonomous expenditure variables).
For GDP to be stable injections have to equal leakages (this can be converted into growth terms to the same effect). The national accounting statements that we have discussed previous such that the government deficit (surplus) equals $-for-$ the non-government surplus (deficit) and those that decompose the non-government sector in the external and private domestic sectors is derived from these relationships.
So imagine there is a certain level of income being produced - its value is immaterial. Imagine that the central bank sees no inflation risk and so interest rates are stable as are exchange rates (these simplifications are to to eliminate unnecessary complexity).
The question then is: what would happen if government increased spending by, say, $100? This is the terrain of the multiplier. If aggregate demand increases drive higher output and income increases then the question is by how much?
The spending multiplier is defined as the change in real income that results from a dollar change in exogenous aggregate demand (so one of G, I or X). We could complicate this by having autonomous consumption as well but the principle is not altered.
So the starting point is to define the consumption relationship. The most simple is a proportional relationship to disposable income (Yd). So we might write it as C = c*Yd - where little c is the marginal propensity to consume (MPC) or the fraction of every dollar of disposable income consumed. We will use c = 0.8.
The * sign denotes multiplication. You can do this example in an spreadsheet if you like.
Our tax relationship is already defined above - so T = tY. The little t is the marginal tax rate which in this case is the proportional rate (assume it is 0.2). Note here taxes are taken out of total income (Y) which then defines disposable income.
So Yd = (1-t) times Y or Yd = (1-0.2)*Y = 0.8*Y
If imports (M) are 20 per cent of total income (Y) then the relationship is M = m*Y where little m is the marginal propensity to import or the economy will increase imports by 20 cents for every real GDP dollar produced.
If you understand all that then the explanation of the multiplier follows logically.
Imagine that government spending went up by $100 and the change in real national income is $179. Then the multiplier is the ratio (denoted k) of the Change in Total Income to the Change in government spending.
Thus k = $179/$100 = 1.79.
This says that for every dollar the government spends total real GDP will rise by $1.79 after taking into account the leakages from taxation, saving and imports.
When we conduct this thought experiment we are assuming the other autonomous expenditure components (I and X) are unchanged.
But the important point is to understand why the process generates a multiplier value of 1.79.
Here is a spreadsheet table I produced as a basis of the explanation. You might want to click it and then print it off if you are having trouble following the period by period flows.
So at the start of Period 1, the government increases spending by $100. The Table then traces out the changes that occur in the macroeconomic aggregates that follow this increase in spending (and "injection" of $100). The total change in real GDP (Column 1) will then tell us the multiplier value (although there is a simple formula that can compute it). The parameters which drive the individual flows are shown at the bottom of the table.
Note I have left out the full period adjustment - only showing up to Period 12. After that the adjustments are tiny until they peter out to zero.
Firms initially react to the $100 order from government at the beginning of the process of change. They increase output (assuming no change in inventories) and generate an extra $100 in income as a consequence which is the 100 change in GDP in Column [1].
The government taxes this income increase at 20 cents in the dollar (t = 0.20) and so disposable income only rises by $80 (Column 5).
There is a saying that one person's income is another person's expenditure and so the more the latter spends the more the former will receive and spend in turn - repeating the process.
Households spend 80 cents of every disposable dollar they receive which means that consumption rises by $64 in response to the rise in production/income. Households also save $16 of disposable income as a residual.
Imports also rise by $20 given that every dollar of GDP leads to a 20 cents increase imports (by assumption here) and this spending is lost from the spending stream in the next period.
So the initial rise in government spending has induced new consumption spending of $64. The workers who earned that income spend it and the production system responds. But remember $20 was lost from the spending stream so the second period spending increase is $44. Firms react and generate and extra $44 to meet the increase in aggregate demand.
And so the process continues with each period seeing a smaller and smaller induced spending effect (via consumption) because the leakages are draining the spending that gets recycled into increased production.
Eventually the process stops and income reaches its new "equilibrium" level in response to the step-increase of $100 in government spending. Note I haven't show the total process in the Table and the final totals are the actual final totals.
If you check the total change in leakages (S + T + M) in Column (6) you see they equal $100 which matches the initial injection of government spending. The rule is that the multiplier process ends when the sum of the change in leakages matches the initial injection which started the process off.
You can also see that the initial injection of government spending ($100) stimulates an eventual rise in GDP of $179 (hence the multiplier of 1.79) and consumption has risen by 114, Saving by 29 and Imports by 36.
The following blog post may be of further interest to you: