Suppose we have a Keynesian economy in which output (real GDP) is well below the full employment level.
Y = real GDP = $500 billion
C = consumption = $400 billion
G = government real purchases = $50 billion = T, taxes
I = investment = $50 billion = S, saving.
There is no foreign trade. The marginal propensity to consume is 0.80, i.e. 80 cents of each extra $1 of income is spent on consumption. Taxes do not vary with income.
Real output (GDP) is $500 billion; Aggregate Expenditure is (C +
I + G) [there is no foreign trade]is $ 400 + 50 + 50 equals $500 billion.
So output equals expenditure on output, the economy is in macroeconomic
equilibrium.
c) What is the multiplier in this economy?
The multiplier is one over [one minus the mpc], i.e. 1/(1 - 0.8) equals 1/(0.2) equals 5.
d) When the economy reaches a new equilibrium, what is the new level of GDP?
Equilibrium change in output equals the multiplier times the initial change in expenditure on income, i.e. 5 times $5 billion equals $25 billion. So new level of GDP is $500 + $25 billion, equals $525 billion.
e) What will saving then be?
In this model, taxes don't change with income, so the marginal propensity
to consume and the marginal propensity to save must add to one [the only
things households can do with income are spend it on consumption or save
it]. The mpc is 0.8, so the mps is 0.2, i.e. 20 cents of each extra $1
of income is saved. Income went up $25 billion, so savings go up 0.2 times
$25 billion equals $5 billion, the new level of saving is $50 + $5 equals
$55 billion.
Now we change things a bit:
Suppose we have a Keynesian economy in which output
(real GDP) is well below the full employment level.
Y = real GDP = $500 billion
C = consumption = $400 billion
G = government real purchases = $50 billion = T, taxes
I = investment = $50 billion = S, saving.
There is no foreign trade. The marginal propensity
to consume is 0.80, i.e. 80 cents of each extra $1 of income is spent on
consumption. Taxes do not vary with income.
No change from above, same answer, yes it is.
c) Is there an immediate effect on income?
No; the change in income only comes about from the effect of the change in consumption spending.
d) Can you figure out what the multiplier would be for this change?
It is not obvious immediately, given what we have done. We return to this after answering the next part of the problem.
e) When the economy reaches a new equilibrium, what is the new level of GDP?
The difference between this situation and the first problem is what
happens initially. If you think of this in terms of the circular flow diagram,
and then the effects, we have something like this:
| First Problem -- I increases $5 bn | Second Problem -- T decreases $5 bn | |||
| Effect on | Y | C | Y | C |
| First Round | + 5 bn | + 4 bn | Nothing | + 4 bn |
| Second Round | + 4 bn | + 3.2 bn | + 4 bn | + 3.2 bn |
| Third Round | + 3.2 bn | + 2.56 bn | + 3.2 bn | + 2.56 bn |
| Fourth Round | + 2.56 bn | + 2.048bn | + 2.56 bn | +2.048 bn |
| Fifth Round | + 2.048 bn | Etc | Etc | Etc |
| Etc | ||||
The impact as the effects of the injection of extra spending works its
way round and round the circular flow is identical, EXCEPT in the very
first round, where the tax cut has no impact itself on output and income,
it works its effect through the households' disposable income, what
it has left after taxes for the same initial level of output and income.
So, in the first case, the final equilibrium change in income and output,
the sum of the first Y column extended to infinity, was the multiplier
times the initial change, 5 time $5 bn equals $25 billion. In the second
problem, the final equilibrium change is the sum of the second Y column
extended to infinity, which is the same as the first EXCEPT for the $5
bn in the first round which is not there in the second case. So the final
equilibrium change in this second problem is going to be $25 bn less $5
bn, which is $20 bn, so the new level of GDP will be $500 bn plus $20 bn
which is $520 bn.
Now we can answer (d) above. The multiplier is (final, equilibrium,
change in income and output)/(initial change that causes it), or the amount
one multiplies the initial change by to get the final equilibrium change
in income and output. So here it is $20bn/$5bn equals 4; the tax cut multiplier
is 4, or one less than [1/(1 - mpc)], because in the first round the immediate
impact of the tax cut on income and output is nothing -- it only impacts
household disposable income and consumption in the first round, whereas
an increase in investment (or government purchases) has an equal impact
on income and output immediately in the first round (because they are part
of aggregate expenditure themselves).
Now consider the third problem, where we change the numbers a bit:
Suppose we have a Keynesian economy in which output (real GDP) is well below the full employment level.
Y = real GDP = $800 billion
C = consumption = $600 billion
G = government real purchases = $100 billion = T, taxes
I = investment = $100 billion = S, saving.
There is no foreign trade. The marginal propensity to consume is 0.75, i.e. 75 cents of each extra $1 of income is spent on consumption. Taxes do not vary with income.
Yes. Because real GDP (output) is $800 billion, and
Aggregate Expenditure (C + I + G) [no foreign trade, remember] is $ 600
+ 100 + 100 = $800 billion, Y = AE, we are in equilibrium.
c) What is the multiplier in this economy?
Multiplier is [1/(1 - mpc)], i.e. one divided by (1 - 0.75), 1/(.25), equals 4.
d) What is the new equilibrium level of Y?
Initial change in spending on output is $25 billion;
Change in equilibrium spending and output is initial change times the multiplier, i.e. 4 x $25 billion equals $100 billion;
So new equilibrium is 800 + 100 = $900 billion.