Keynes and National Income Multiplier
Keynes and National Income Multiplier
Keynes and National Income Multiplier
Junior College
Vince Sammut
John Maynard Keynes (1883-1946)
As World War II was drawing to a close, Keynes arrived in the U.S. State of New Hampshire
as the most important member of the British delegation to the famous Bretton Woods
conference, a conference that established an international monetary system; a system that
provided the world economy with much-needed stability for a whole generation. According to
the agreement reached, countries would retain fixed exchange rates against the dollar, while
1
Keynes’s concern over the vindictive terms imposed on the defeated Germans in the World War I Treaty of
Versailles was vindicated by the rise of Adolf Hitler; and the memory of his warnings helped convince the
victorious Allies of WW II to aid, not punish, their enemies.
In 1936, Keynes had published The General Theory of Employment, Interest and Money, a
book that revolutionised economic theory in the same way that Charles Darwin’s The Origin
of Species revolutionised biology. This so-called Keynesian revolution was grounded in a
new theory of income determination; a theory based on the concept of:
The consumption function referred to a relationship between total consumer spending and
national income, such that consumer spending always rises less than proportionately with
income, leaving a savings gap that only private or public investment can fill. The liquidity
preference theory of interest emphasised the role of interest rates as the reward for doing
without the advantages of money as the only perfectly liquid asset. The inflexibility of money
wages, the most controversial of Keynes' leading principles, was grounded on a realistic
appreciation of labour markets in a modern industrial economy.
With the General Theory, as it became known, Keynes sought to develop a theory that could
explain the determination of aggregate output - and as a consequence, employment. Among
the revolutionary concepts initiated by Keynes was the concept of a demand-determined
equilibrium wherein unemployment is possible, the ineffectiveness of price flexibility to cure
unemployment, a unique theory of money based on "liquidity preference", the introduction of
radical uncertainty and expectations, the marginal efficiency of investment schedule breaking
Say's Law (and thus reversing the savings-investment causation), the possibility of using
government fiscal and monetary policy to help eliminate recessions and control economic
booms. Indeed, with this book, he almost single-handedly constructed the fundamental
relationships and ideas behind what became known as "macroeconomics".
Before the General Theory, economists could not explain how economic depressions happen,
or what to do about them. After 1936, they could. Full employment, Keynes concluded, could
be maintained in a capitalist economy but only if governments are willing to incur counter-
cyclical budgetary deficits to offset the inbuilt tendency towards private over-saving. For a
stretch of about 25 years, many economists turned their backs on Keynes. They claimed, with
some justice, that he made assumptions that could not be rigorously justified. Moreover, the
problems facing the world in the 70s and 80s were non-Keynesian in nature; inflation rather
than deflation, inadequate saving rather than deficient demand. For a while various anti-
Keynesian ideas - ranging from mathematically impeccable academic demonstrations that
recessions cannot happen, to popular doctrines like supply-side economics - seemed to have
crowded Keynes off the stage.
Yet, just take a look at the current world situation (2000 – 2004), particularly at Japan - an
economy that has clearly been suffering from a lack of demand, not supply, where the clear
and present danger is deflation, not inflation. In the face of this reality, how can anyone say
that Keynesian ideas are no longer relevant? The essential truth of Keynes’s big idea - that
even the most productive economy can fail if consumers and investors spend too little, that
the pursuit of sound money and balanced budgets is sometimes (but not always!) foolish
rather than wise - is as evident in today’s world as it was in the 1930s. In addition, in these
dangerous days, we ignore or reject that idea at the world economy’s peril.
Keynesian theory can be illustrated in terms of the circular flow of income; a model
showing the flows of money around the economy. The economy is conventionally split
into firms and households and the circular flow shows the movement of money between
these groups. From households to firms there is a flow of consumption expenditure which
results in a flow of income from firms to households. This income may be in the form of
rent, wages, interest or profit.
For example, if for some reason there is an increase in injections (perhaps through an
increase in investment, government expenditure or exports), an imbalance between
leakages and injections would occur. As a result of this extra aggregate demand, firms
would employ more people. This would mean more income in the economy, some of
which would be spent and some saved, or paid in tax, or spent on imports. The extra
spending would prompt firms in the economy to produce even more, leading to even
more employment and therefore even more income. This process would go on, and on,
and on, until it stopped! It would eventually have to stop because each time income
increased, the level of leakages (savings, tax and imports) also increased. Once leakages
and injections were equal again, equilibrium would be restored. This process, called the
Multiplier effect, has very important implications for economic planning and
macroeconomic policy.
Note that income (Ye) is not fixed; it fluctuates in relation to the cumulative cycles of
declining or increasing production.
For Keynes there was a difference between equilibrium income (the level toward which
the economy gravitates in the short run) and potential income (the level of income that
the economy is technically capable of producing, without generating accelerating
inflation).
Keynes argued that relying on markets to get to full employment was not a good idea. He
believed that the economy could settle at any equilibrium and that there would not be
automatic changes in markets to correct this situation.
The main Keynesian theories used to justify this view were:
According to Classical theory, when the demand for labour falls from D1 to D2 (perhaps
due to the onset of a recession), the wage rate should fall in order for the market to clear.
However, Keynes argued that because wages were sticky downwards, this would not
happen and an unemployment level of ab would persist. This unemployment he termed
demand deficient unemployment.
The Multiplier
Any increase in aggregate demand in the economy would result, according to Keynes, in
an even bigger increase in National Income. This process comes about because any
increase in demand would lead to more people being employed. If more people were
employed, then they would spend the extra earnings. This in turn leads to even more
spending, which leads to even more employment, which leads to even more income and
which would then lead to even more spending, which then leads to ................. The length
of time this process went on for would depend on how much of the extra income was
spent each time. If the initial recipients of the extra income saved it all, then the process
would stop very quickly as no-one else would get their hands on the extra income.
However, if they spent it all, the knock-on effects of the extra spending would carry on
for some time.
Therefore the higher the level of leakages, the lower the multiplier would be. The precise
formula for calculating the multiplier in a two sector closed economy is:
1
Multiplier =
1 - Marginal propensity to consume
A MACROECONOMIC IDENTITY
Y=C+S+T
€20,000 €20,000 0
The table shows that if expected income rises by €2,000, from €10,000 to €12,000, people
will increase their spending by €1,500, or that they will only spend three-fourths of
additional income that they expect to receive. This fraction of additional income that
people spend has a special name; the marginal propensity to consume (or mpc for
short). In the table above the mpc is always three-fourths or 0.75. Thus if income
In addition, economists often talk of the marginal propensity to save, which is the
fraction of additional income that people save. Since people either save or consume
additional income, the sum of the marginal propensity to save and the marginal
propensity to consume should equal one.
The value of the marginal propensity to consume should be greater than zero and less
than one. A value of zero would indicate that none of additional income would be spent;
all would be saved. A value greater than one would mean that if income increased by
€1.00, consumption would go up by more than a euro, which would be unusual
behaviour.
The consumption function can also be illustrated with an equation or a graph. The
equation that gives the consumption function in the table above is:
Where €5000 is autonomous consumption and (3/4) * (expected Income) is induced consumption.
Proof:
S = Y – C, where C = a + bY
C = a + bY
S = Y – (a + bY)
S = – a + (1 – b) Y
S = Y – a – bY
C + S = 0 + bY + (1 – b) Y
S = – a + Y – bY
C + S = (b + 1 – b) Y
S = – a + (1 – b) Y
C + S = Y and
S=–a+sY
b+s=1
where: b = MPC and s = MPS
Thus, if people expect an income of €10,000, this equation says that consumption will be:
What assumptions should be made about how business makes investment decisions?
• One could assume that, like consumption spending, business investment decisions
depend on expected income. The logic of the accelerator principle suggests this
assumption. (For a more detailed explanation of the ‘accelerator’ see notes by Mr. Paul Libreri)
• It could also be assumed that interest rates, which measures the opportunity cost
of tying up assets in the form of capital, should matter.
In the table below investment spending has been added to the model. At an expected or
planned income of €20,000, consumers will spend €20,000 and expect to save nothing.
Business will invest €2,500. Thus actual income will be €22,500 (and due to a reduction
in stocks, realised or actual investment will be 0, matching savings). Since actual income
will not equal expected income, expected income should change, causing behaviour to
change too. Not until the economy expands and planned income equals €30,000 will
expected income equal actual income and only then will behaviour stop changing.
Note that the addition of €2,500 in investment increased the equilibrium from €20,000 to
€30,000. There is a multiplier effect here, and the multiplier is four. The reason for the
multiplier effect can be seen intuitively. As the result of the addition of the $2,500 in
investment, actual income rises by €2,500. Expected income will also rise. But at the new
expected income of €22,500, people will want to spend more than €20,000 for
consumption, so there will be an additional induced increase in spending. But the story
does not end here. The additional consumption increases actual income, and thus
expected income too. This changes behaviour still further. The chain reaction that the
addition of investment sets into motion diminishes at each step, as the total approaches
€30,000. This model is illustrated graphically below.
The only alteration is that the total spending line now includes investment as well as consumption.
As before, the equilibrium exists when expected income equals actual income.
Y=C+I
C = a + bY
Proof:
To complete the standard textbook model, we need to add the third variable: government.
Government affects the flow of spending in two ways:
• it adds spending in the form of government purchases of goods and services and
• it takes money from the flow of spending through taxes.
Government spending affects the model in exactly the same way as investment spending does, but
the addition of taxes forces some changes in the model. Because government spending enters the
model in exactly the same way as investment spending, changes in it have the same multiplier
effects as do changes in investment spending. Adapting the graph to the addition of government
spending is equally easy. The line in the graph above which is called "C+I" will now be called
"C+I+G". Equilibrium will occur where this line crosses the 45° line.
Figure 6: The same result is observed if savings and taxation (W) are correlated with injections (J)
But for the sake of simplicity, the only adjustment to be made in this model is direct
taxation. Disposable income will be total income less taxes. Note that increases or
decreases in taxes will change the relationship between expected income and
consumption. This is illustrated in the table below.
From expected income in column one, taxes are subtracted to give an expected
disposable income. The consumption decisions in column four are based on this expected
disposable income. The next two columns showing investment and government spending
are similar to the fourth column in Table Two.
The addition of government spending and taxes gives government a role in determining
the level of national income. In this model, when government increases spending by
€1.00, income rises by more than a euro because of the multiplier effect. When
government increases taxes, expected disposable income decreases and people reduce
consumption. Through the multiplier process, national income falls by a multiple of the
change in taxes. The use of discretionary or automatic changes in government spending
or taxation, with the goal of changing national income, is called fiscal policy.
The multipliers for government spending and for taxes are not the same and the table
above can help illustrate why they are not. As it stands, the equilibrium level of income is
€22,500, which results when expected disposable income is €20,000. Suppose taxes are
reduced to zero. What will happen to equilibrium income? The tax column becomes zero
and expected disposable income would then equal expected income.
The first two columns of the table can then be ignored, and the third column can be re-
labelled as expected income. Clearly the new equilibrium income will be €30,000. Thus a
Suppose that government spending increases by €2,500. Then the sixth column would
have the value of €4,500, and actual income would be larger in each row. In particular, in
the fourth row, actual income would increase to €32,500. However, expected income in
the fourth row is €32,500, so this row contains the new equilibrium values. Hence an
increase in government spending of €2,500 increases actual income by €10,000 (from
€22,500 to €32,500), or each euro of increased government spending increases actual
income by a multiple of 4.
Changes in government spending and taxes both have the same effects on consumption in
this table. A one euro increase in government spending increases consumption spending
by three, as does a one euro decrease in taxes. The reason that they have different
multiplier effects is that the change in government spending not only induces a change in
consumption but also gets counted in spending, whereas the change in taxes does not get
counted.
This is because taxation does no have a direct impact on spending, while government
spending does. For example, a tax cut would increase disposable income, which is then
likely to lead to added consumption spending. Income will then increase by a multiple of
the decrease in taxes. However, due to the fact that the tax multiplier for a change in taxes
is smaller than the multiplier for a change in government spending, the GDP equilibrium
will change in relation to government expenditure by a multiplier coefficient of one.
The logic behind the balanced budget multiplier being always equal to a coefficient of 1
is explained below.
The Government tax multiplier is the ratio of the change in the equilibrium level of output
to a change income tax:
1 MPC
∆ Y = ( − ∆ T × MPC ) × = − ∆T ×
MPS MPS
MPC
Tax multiplier ≡ −
MPS
If one combines the effects of the government spending multiplier with the tax multiplier:
1 − MPC MPS
+ = =1
MPS MPS MPS
From this equation, one may see that consumption is less by (-bTo - btY) than what it
would have been without taxation. Graphically, the imposition of taxes would shift the
consumption function downwards. So if the government expenditure multiplier = 1/(1-b)
and, the government taxation multiplier = -b(1-b); then a balanced budget would
stimulate the economy by a combined multiplier coefficient of 1.
In other words, a simultaneous increase in government spending by €1m and direct taxes
by €1m will increase equilibrium income by €1m. The reason for this is that the
government would be collecting in taxation some income that would otherwise have
leaked out of the circular flow of income, but it would be spending all of this income.
• A high propensity of withdrawals: The greater the level of leakages from the circular
flow of income the lower the multiplier coefficient. This is typically the case for small
island economies such as Malta, due to their high dependence on imports.
• Automatic stabilizers: When the economy expands and income increases, the amount of
taxes collected increases, offsetting some of the expansion
• The interest rate: All else remaining the same, an increase in government spending
causes the interest rate to increase, crowding out consumption and investment
expenditures.
• The response of the price level: Expansionary policy leads to an increase in the price
level, which reduces the multiplier, particularly when the economy is on the steep part of
the AS curve.
• There are excess capital and excess labour: Output can increase by putting excess
labour and capital back to work. Hence less investment is required.
• There are stocks or inventories: To the extent that firms draw down their inventories in
the short run in response to an increase in demand, output does not respond as quickly to
demand changes.
• The life-cycle hypothesis and household expectations: The multiplier effects for policy
changes, such as tax-rate changes, that are perceived by households to be temporary are
smaller than long term ones.
Figure 7: The ‘Life-cycle’ (Franco Modigliani) and ‘Permanent Income’ (Milton Friedman)
theories of consumption are an extension of Keynes's theory. They state that households
make lifetime consumption decisions based on their expectations of lifetime income.
The diagram below illustrates the cause and effect relationship between variables,
sometimes referred to by economists as the feedback2 loop. This is central in the income-
expenditure model. Consumption, investment, and government spending determine actual
income. Actual income and taxes determine expected disposable income, and finally
expected disposable income determines what consumption will be.
The feedback loop is the reason why investment and government spending have
multiplier effects. A drop in investment, for example, begins by reducing actual income
by the amount of the drop. Then the lower level of actual income changes expected
income, and consumption also declines. Hence a €1.00 decline in investment will,
according to the logic of this model, cause a decline in income of more than €1.00.
It has been stated that the equilibrium condition for this model is that expected income
must equal actual income. There is another way of looking at this equilibrium condition.
Expected income can be divided into three parts. First some is removed as taxes, and then
what is left is divided between consumption and expected savings, or:
Yexp = T + C + Sexp
It has also been argued that actual income is made up of three types of spending:
consumption, investment, and government spending, or:
Yact = C + I + G
T + C + Sexp = C + I + G
2
The concept of feedback provides a way to view the functions of price in allocating scarce resources. A
system of feedback exists when two variables are interrelated, so that a change in variable A affects variable
B, but, in turn, a change in variable B affects variable A.
Sexp + T = I + G
In other words, this equation says that equilibrium exists at that level of income for which
the amount people intend to withdraw from the flow of spending either as taxes or
savings just equals the amount they intend to add to the flow of spending as investment or
government spending.
National income equilibrium can be illustrated with an analogy to a leaky bucket. In the
leaky bucket higher levels of water create more pressure and thus faster leakage. An
equilibrium level of water occurs when the leakage just equals the inflow of water, and
the water line remains stable.
In the income-expenditure model, investment and government spending are inflows and
taxes and expected saving are leakages. As income increases, so does leakage in the form
of expected savings. Just as there will be only one level of water in the bucket for which
leakages will equal inflows, so there will be only one level of income in the model for
which leakages will equal inflows.
In the top part of the illustration below, the difference between the C and the C+I+G lines
is investment plus government spending, which the bottom part graphs separately as the
I+G line. Because the distance between the C line and the C+I+G line is constant in the
top part, the I+G line is flat in the bottom part. In other words, investment and
government expenditure are considered as autonomous variables. The difference between
the 45° line and the C line is the difference between expected income and consumption,
Equilibrium exists when the C+I+G line crosses the 45° line. At this level of expected
income, the distance between the C and the C+I+G lines (which is investment plus
government spending) just equals the distance between the C line and the 45° line (which
is savings plus taxes). Thus equilibrium exists when investment plus government
spending equals expected savings plus taxes.
Suppose people decide to become thriftier, that is, they decide to save more at each level
of income. One might expect that this would increase the total amount of savings, but the
simple income-expenditure model predicts a paradox of thrift, that total savings will
remain the same and income will decline. If people become thriftier, they consume less at
each level of expected income. On a graph, this increased thriftiness can be illustrated as
a shift downward of the consumption function or a shift upward of the savings function. If
one draws in these shifted lines, one would see a fall in the income equilibrium.
The diagram below shows the economy at a stable equilibrium, where I is in actual fact
not purely autonomous but also induced; that is, it is also positively related with
consumption. I is at a level that maximises output on the production possibility boundary.
Hence, no deflationary or inflationary pressures exist. Furthermore, factor markets such
as labour and loanable funds are ‘cleared’ at market rates. Hence, no resource shortages
or surpluses exist either.
Note what happens when households become ‘thrifty’ and increase their savings:
• The “a” in C = a + bY decreases, which means that the demand function shifts
downwards.
In other words, if a large number of people in the economy suddenly decided to save
more and consume less, total spending would fall and unemployment would rise.
Paradox of thrift
Trying to save more does not
result in more saving.
Consider what would happen if the savings hole in the leaky bucket analogy is made a
little larger, which corresponds to people becoming thriftier. Initially there will be a larger
outflow of water. But this cannot continue indefinitely. Equilibrium exists when the
inflow equals the outflow, and the inflow has not changed. This means that the water
level must drop so that the pressure forcing water out of the bottom will be reduced. Less
pressure means less outflow, and at some lower level of water, equilibrium will be re-
established.
Many early followers of Keynes, and probably Keynes himself, believed that a lack of
spending was likely to be a chronic problem in an industrialised economy, and therefore
they thought that measures should be taken to reduce savings. Since the rich did most of
the saving, an obvious solution was to tax the rich to reduce their incomes and thus their
savings. Those who had wanted to tax the rich with the goal of equalising incomes had,
prior to Keynes, been confronted with the argument that such a move would have harmful
effects on growth. It is not surprising that they were often eager to embrace a theory that
implied that equalising incomes had only good side effects. This partially explains the
popularity of Keynesian economics with socialist or centre-left politicians.
Fiscal Policy
The use of government spending
and taxes to influence GDP,
employment, and the price level.
AD = C + I + G + (X-M)
Keynes rejected the view of Adam Smith that left alone, a market system generally
functions well, or that the "invisible hand" works. The simple income-expenditure model
suggests that what happens in the market for goods and services is the key to
understanding macroeconomic problems; but in analysing this market, it completely
ignores prices. Price level is not determined within the Keynesian model, and generally it
was assumed to be constant. Assuming fixed prices ignores the primary way that
adjustment to equilibrium happens in microeconomics. Assuming prices constant or
fixed, puts the Keynesian model on a conflicting path with microeconomic theory.
If there is unemployment, microeconomic theory suggests that wages will fall, and this
will change the amount of unemployment. If it is assumed that prices are in fact not very
If the aggregate-supply curve is horizontal, the model can say nothing about price change,
which is a severe limitation because inflation is one of the variables macroeconomics
SLOMAN, J., WRIDE, A. (2009) Economics. 7th edition. Essex, U.K: Pearson Education Ltd
STANLALKE, G.F. (1984) Macro Economics. 3rd edition. Essex, U.K: Longman Group Ltd.
TAYLOR, K.S. (2001) Human Society and the Global Economy, [Online] Available
from: http://online.bcc.ctc.edu/econ100/ksttext/chaplist.htm [Accessed: 10th May 2004]