We’ve been examining
what happens if aggregate demand (C+I+G) happens to not equal total income
(Y). If these quantities are equal, business expectations are met, everything is sold in the
quantities anticipated at the prices anticipated, and GDP has no tendency to
change. Should Aggregate Demand be less
than incomes paid out, there will not be enough spending to buy up everything
businesses intended to produce.
Business will see inventories accumulating and decide to cut back on
production; perhaps even laying people off.
With less production (and employment) households have less income to
spend, so Aggregate Demand (which was inadequate to start with) further
declines. This leads to more cuts in
production and employment, more reduction to household income and further
declines in Aggregate Demand. We have a
recessionary spiral.
On the other hand,
Aggregate Demand might exceed paid out income.
I realize this sounds a bit odd (how do we have spending in excess of
income) but it can easily happen. Under
these circumstances, total spending is running ahead of business
expectations. Business will see
declining inventories, and increase output and employment. As a result, households will have more
income and will spend more. This
further increases Aggregate Demand and causes sales to continue to run ahead of
business expectations which will cause further increases in output and employment. As we approach full employment, prices will
begin to rise and inflationary pressures will appear. We will have entered an inflationary spiral. The closer we get to full employment, the
greater the rate of inflation will become.
Once started, how do
these recessionary and inflationary spirals come to an end? The easiest answer to this question focuses on the relationship between
savings and investment (ignoring, for now, government). If Aggregate Demand is less than paid out
incomes, GDP will fall. Aggregate
Demand will be less than incomes because Saving (-) is greater than Investment
(+)—the leakages (-) to the income stream exceed the injections (+). As long as this is true, GDP will continue
to fall because Aggregate Demand will continue to be inadequate to buy up what
businesses plan on producing. There is
an answer, however. Savings do not
remain constant as incomes fall. In
fact, savings decline as income declines.
So, if the problem is that savings exceed investment, then if investment remains constant (assumed for
the sake of discussion), savings will come to equal investment again as savings
decline in response to falling incomes.
The degree of decline in GDP depends on how rapidly savings change when
incomes change.
In the case of an
inflationary spiral, the problem is that Investment (+) exceeds Savings (-), the injections (+) to the income
stream exceed the leakages (-). As
incomes rise, however, Savings (-) will increase until thy again come into
equality with investment (which we are again assuming stays constant). Once again, the change in GDP depends upon
how rapidly Savings(-) change as incomes change.
The relationship
between savings and income is illustrated by what we call a Consumption
Function. The Consumption Function
reflects the fact that as income changes, consumption changes (and so, by
extension, does saving). A consumption
function has the following general appearance:
The graph above shows us a Consumption Function in a simple, linear configuration. The line “C” shows that as income rises, consumption rises as well. Obviously, since income funds the consumption, spending can’t increase by more than one dollar for every dollar increase in income. If a consumer were to spend no part of an additional dollar of income, then the slope of the consumption function would be zero. Thus, the slope (rise over the run) of the curve “C” must be lie between zero and one. The slope of the consumption function is called the MARGINAL PROPENSITY TO CONSUME (MPC), and is the fraction of an additional dollar of income that is consumed. Since a person can either save or spend an additional dollar of income, any increase in income not spent must be saved. Therefore there exists a parallel savings function of the form shown below:
The plus and minus savings labels refer to the fact that savings can be negative, that is, you can “dip into” your savings. In this graph, people are “dipping into” savings for about half the length of the Savings function (S-S). In the consumption function graph above the savings graph, you can see that at zero income, there is positive consumption. The negative savings shown in the savings graph at the zero income level is funding this positive consumption.
We can use the savings function to illustrate the statements made above about the level of savings (when unequal to investment) rising or falling in response to a change in income, and coming back into equality with investment as a result of doing so.
Have a look at the graph below:
The graph, above, shows two savings functions and an investment line. The investment line stays at a constant height showing that investment is assumed, here, not to fluctuate with income. At the original savings level shown by savings function S-S, savings equals investment at the income level shown as Y. The economy is in equilibrium, injections equal leakages, and GDP has no tendency to move. Now, if savings were to increase to a level shown by savings function S1-S1, then at income level Y, savings significantly exceed investment. GDP will fall. As GDP falls, savings shown on S1-S1 also fall until they come into equality with investment again at income level Y1. Note that income appears to have fallen about $3 for each dollar decline in savings. The fact that a change in savings of one dollar causes a change of, say, $3 in income is called the MULTIPLIER EFFECT.
You can read the graph, above, in another way as well. Let’s assume that we started out with savings as shown on S1-S1. In this case, equilibrium GDP would occur at income level Y1 (here savings equal investment). Now, assume people decreased their savings (increased the consumption) so that savings were now at a level shown by curve S-S. At the original equilibrium level of GDP, Y1, investment is now greater than savings as shown on savings curve S-S. Because investment exceeds savings, income will rise. The rise will continue until savings S-S come once more into equality with investment which occurs at income level Y. Note that every dollar’s decrease in savings (increase in consumption) leads—in this example—to about a $3 increase in income. That’s the multiplier effect again.
The multiplier effect varies with the rate at which savings changes as incomes change. That rate is equal to the slope of the savings function, and is called the MARGINAL PROPENSITY TO SAVE (MPS). The MPS is also equal to 1 minus the MPC. That is, if a person consumes 80 cents out of each additional dollars of income, then his MPC is equal to 0.8. Since he spends 80 cents, that means he doesn’t spend, or saves, 20 cents. The MPS, then, is equal to 1 – 0.8 or 0.2. The person saves an additional 20 cents out of each dollar of additional income. If his income decreases by a dollar, he will reduce his rate of spending by 80 cents and his rate of savings by 20 cents.
If savings change, for example, by 20 cents for every dollar change in income, that means that to eliminate, say, $1,000,000 of excess savings, income would need to fall by 1/0.2 (5) times the $1,000,000 in required savings reduction—or by $5,000,000. Similarly, if people decided to reduce their savings (e.g. increase consumption) by $100,000,000, that would mean that income would increase, and would do so as long as savings are less than investment. Since savings are, initially, $100,000,000 less than investment, we would need to generate $100,000,000 in additional savings to bring them into equality with investment again. Since we get only a 20 cent increase in savings for each dollar increase in income, we’d have to have a 5 dollar income increase to generate a one dollar increase in savings. That suggests we need a 5 x $100,000,000 or $500,000,000 increase in GDP to get the added savings we require.
In general, the MULTIPLIER is computed by multiplying 1/MPS times the change in spending or saving. Since the MPS = 1-MPC, the multiplier can also be computed as 1/(1-MPC).
The MULTIPLIER EFFECT can also be viewed from the consumption side, rather than from the savings side as we have been doing. A dollar of increased spending always generates more that a dollar increase in income. Consider the following, if the government were to increase its spending by $1 billion, (with out increasing taxes), that would immediately create $1 billion in new income (GDP) for folks that receive the spending. Maybe the government buys 10 new fighter aircraft, so the recipients of the spending are, initially, in the aircraft industry. This, however, is not the end of the story. The people receiving the $1 billion dollars will increase their spending because they now have more income: a billion dollars more to be exact. If the MPC is 0.8, that means that, on average, households will increase their consumption by 0.8 x $1billion, or by $800 million. When they do this, income (GDP) goes up by a further $800 million as people make the goods and services that have been purchased. That spending becomes additional income for those who made and sold the $800 million of goods and services. These folks increase their consumption by the MPC times their increase in income 0.8 x $800 million or $640million. This becomes income to someone else, and the recipients of this income increase their spending by 0.8 x $640 million or by $512million. At each round, the resulting consumption increase (and GDP increase) is 0.8 of the previous one.
The string of spending and income increase looks like 0.8 $1billion + 0.8x(0.8x $1billion) + 0.8 x(0.8x (0.8x $1 billion))) and so one. Obviously, each time you take 80 percent of something, the number becomes smaller. 0.8n x $1billion is a very small number as n gets larger and larger. By the time we’ve reached the 10th round of spending, the effect (at 0.8 MPC) is only 10% of the starting impact. By the 50th iteration, the increase in GDP is only 14 ten thousandths of a percent of its original level. Ultimately, the effect tapers off, effectively, to zero. When it does, the sum of the increments to GDP will equal (1/(1-0.8) x $1billion) which translates to (1/0.2 x $1billion) which becomes (5 x $1billion) or $5billion.
Graphically, the consumption multiplier would look like that shown below:
Each iteration generates an increase to GDP that is 80% of the previous one. Eventually, 80% of the remainder becomes a rather small number, which we are at liberty to ignore. The total of the rectangles in the graph should be $5 billion—and would be if we could draw it carefully enough.
To be really technical about this, the increase in spending has to be a sustained one in order to get an ongoing increase in GDP. In the example above, the government would have to increase its spending by $1billion, and keep spending that billion every year in order to get a sustained increase in the ongoing flow of GDP of $5 billion a year, year in, year out.
Any increase in spending will increase GDP, and will do so by the multiplier times the spending increase. In other words, increases in household consumption, business investment and government deficit (financed not with taxes but by borrowing) spending all increase the level of GDP in exactly the same way and by the same amount. Decreases in all categories of spending tend to lower GDP by the multiplier times the change in spending. Again, this is equally true for household, government (deficit) spending and business spending (investment).
A change in taxes, however, has a slightly different multiplier effect. The tax multiplier is one less than the expenditure multiplier (i.e. (1/(1-MPC))-1). Thus, if the expenditure multiplier is 5, the tax multiplier is 4. If the expenditure multiplier is 4, the tax multiplier is 3. The reason for this has to do with the fact that giving people money (in the form of a tax cut) is not quite the same as spending money. If you give someone a dollar of additional income (say in the form of a tax cut), they won’t increase their spending by $1, but rather they’ll increase spending by the MPC x $1. In the example we’ve been using, that would be 0.8 x $1 or 80 cents. One must remember that it’s the spending that stimulates the economy, and when the government gives a dollar in tax cuts, they don’t see a dollars worth of increased spending, but rather the MPC times the dollar. When the government engages in deficit spending, the immediate change in consumption equals the spending itself. Comparing the effects of spending and tax cuts, we see the following results:
Spending resulting from Gov’t spending and a tax cut of $100 over time:
Government Tax
Iteration Spending Cut
spending1 $100 $0
spending2 $80 $80
spending3 $64 $64
spending4 $51.20 $51.20
spending5 $40.96 $40.96
spending6 $32.77 $32.77
spending7 $26.21 $26.21
spending8 $20.97 $20.97
And on
And on
If you look at the spending streams, the difference between them becomes obvious: it’s the initial $100 increase in the spending column that has no corollary in the tax cut column. The sum of the columns will differ by $100, with the spending column being the larger. In this case, a total summation of the changes would show that the $100 in government spending generated a $500 increase in GDP. The tax cut column will, by simple inspection, total to $100 less, or $400. The spending multiplier is 5 and the tax multiplier is 4.
The difference between the tax and spending multiplier gives rise to what is called the balanced budget multiplier. If the government were to fund all spending with taxes, there would still be a stimulus to the economy. An additional $100 dollars of government spending would generate a $500 increase in GDP. The $100 tax increase to fund the spending would cause a drop in GDP equal to (5-1) or 4 times $100 or a change of -$400. The effect of the $500 increase caused by the spending and the $400 drop in GDP caused by the tax increase would be a net change in GDP of $100 (+$500 - $400). The “balanced budget multiplier” always equals 1.
While we are looking at the multiplier from the consumption side, it is useful to have a look at the graph, below.
The graph above shows the components of spending (aggregate demand) “stacked up” on top of one another. The highest line, C+I+G is the sum of household, business and government spending, and represents aggregate demand. The dark line emitting from the origin is meant to be drawn at 45 degree so that along it the value of spending and income is the same. Since at any point on this line spending and income are equal, this is a line that shows us all the points where aggregate demand equals income (or GDP). Equality of spending and income is a condition of macro equilibrium. When spending equals income, all of the output that business have made will be sold. The intersection of the 45 degree line and the C+I+G curve is the point at which aggregate demand equal aggregate supply (income), and as such shows us the equilibrium level of GDP associated with that level of spending.
Of the three components of spending, only Consumption varies with income. Investment is posited as a constant level of spending, and Government spending depends on the whims of Congress rather than the level of GDP. Because they don’t vary with income, the Investment and Government spending curves are drawn parallel to the Consumption funtion.
One of the things we can demonstrate using the graph is the effect of a change in Government spending. In the graph above, a decline in G has moved the C+I+G curve down to the level shown by C+I+G’. At the new, lower level of spending, the equilibrium GDP drops to the intersection of the 45 degree line with the lower aggregate demand curve C+I+G’. The new equilibrium is shown at Y’ equilibrium.
Armed with this information, we are able to contemplate a few policy issues. Let’s imagine that the economy was experiencing inflation. This suggests that we are trying to buy more than the economy is capable of producing, thus causing prices to be bid up across the board. The problem, clearly, is too much spending. What we need to do is reduce aggregate demand. The question is how, and by how much. Let’s assume we know that the full employment level of GDP is $4 trillion (thousand billion) a year. Assume, further, that the level of spending or aggregate demand is currently $4.25 trillion a year. We have, in short, 0.25 trillion (250 billion) dollars of “excess” spending. In order to eliminate that much aggregate demand we have two tools we can use: government spending and taxation (the basic tools of Fiscal Policy). If we want to eliminate the excess spending using government spending, do we need to reduce government spending by $250 billion? The answer is no. If the MPC is 0.8, we know the spending multiplier is 5. Thus, to get a total reduction in spending and GDP of $250 billion, we need only reduce government spending by $50 billion ($250 billion/5). If we tackle the problem using a tax increase, we would have to increase taxes by $62.5 billion or ($250 billion/4). We could also use both tax increases in spending reduction so long as (5 x spending change) + (4 x tax change) = -$250 billion.
We can use the same tools, in the same way, to stimulate a faltering economy. Let’s assume that full employment GDP is (once again) $4 trillion. For the sake of illustration, we assume the current level of GDP is $3.6 trillion. We need to generate an additional 0.4 trillion dollar ($400 billion) in spending. To do this we increase government spending by $80 billion ($400/5) or decrease taxes by $100 billion ($400/4) or some combination of both.
Given that the economy currently seems to be slipping into a recession—moving away from full employment GDP—a tax cut or increase in government spending (or both) would be in order. What the government has been doing, instead, is reducing the interest rates. This constitutes an example of Monetary Policy as opposed to Fiscal Policy. We’ll be taking up Monetary Policy following the mid-term.
We should keep in mind the fact that this analysis is pretty basic. This simple Keynesian model assumes, for example, that consumption is a simple linear function of current income. Other economists have developed far more complex relationships between consumption and several variables aside from current income. One theory, for example, posits that consumption is only increased in response to changes in what consumers see as their Permanent Income. To the extent this is true, the effect of the multiplier is reduced since increases in spending take longer to develop in response to an increase in income.
We’ve assumed, further, that the government can borrow for deficit spending without displacing other, private borrowing. To the extent that government borrowing is at the expense of private borrowing and spending (this is called “crowding out”), the effect of deficit spending is reduced. In this case, government spending just replaces private spending which would have occurred on its own, and so there is no net stimulus to the economy.
We have also assumed that investment decisions are not responsive to the interest rate or to the level and rate of change in GDP. These assumptions need to be relaxed in order to have a sophisticated model. Such relaxations are typically discussed in intermediate macro courses.