Chapter 21: The Simplest Short-Run Macro Model
Question 2
a) accumulate; reduce; fall
b) fall; increase; rise
c) investment
d) upward; rise; 45-degree
e) more; simple multiplier (× $10 billion)
f) larger; 1/(1-z)
Question 4
a) Desired saving is equal to disposable income minus desired consumption. We can
compute desired saving (S) from the table in Question 3. The plotted desired saving
function is shown below. The slope of the function is the marginal propensity to save,
∆S/∆YD, which equals one minus the marginal propensity to consume. In this case the
marginal propensity to save is equal to 0.25.
YD
C
S
0
100
200
300
400
500
600
700
800
150
225
300
375
450
525
600
675
750
–150
–125
–100
–75
–50
–25
0
25
50
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b) To show this to be true, begin by noting that disposable income must either be consumed
or saved. Thus
YD = C + S
Now divide both sides by YD to get
1 = C/YD + S/YD
This shows that the average propensity to consume plus the average propensity to save
must equal one.
Question 6
a) When actual national income is Y1, desired aggregate expenditure is b. Actual output is
a and so desired aggregate expenditure exceeds actual output. Inventories are being
depleted — this is unplanned negative inventory investment.
b) The depletion of inventories eventually leads firms to increase the level of output so
they can replenish their inventories. The rise in output generates a rise in income and this
induces an increase in desired aggregate expenditure. We move up and to the right along
the AE curve. But as long as AE exceeds actual output, the depletion of inventories leads
firms to increase output. The economy eventually settles down where AE cuts the 45degree line. At this point actual output is exactly equal to the level of desired aggregate
expenditure, and the level of inventories is constant.
c) When actual national income is Y2, desired aggregate expenditure is d. Actual output is
e and so desired aggregate expenditure is less than actual output. Inventories are being
accumulated — this is unplanned positive inventory investment.
d) The unintended accumulation of inventories eventually leads firms to reduce the level
of output. The reduction in output reduces income and this induces a decrease in desired
aggregate expenditure. We move down and to the left along the AE curve. But as long as
AE is less than actual output, the accumulation of inventories leads firms to reduce
output. The economy eventually settles down where AE cuts the 45-degree line. At this
point actual output is exactly equal to the level of desired aggregate expenditure, and
inventories are neither being depleted nor accumulated.
Question 8
a) The (desired) aggregate expenditure function shows the total desired expenditure at each
level of national income.
AE = C + I ⇒ AE = 1400 + 0.8Y + 400 ⇒ AE = 1800 + 0.8Y
b) Equilibrium requires that Y = AE (this is the equation for the 45-degree line). The
equilibrium level of national income is therefore the value of Y that solves the following
equation:
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Y = 1800 + 0.8Y ⇒ Y(1 – 0.8) = 1800 ⇒ Y = 1800/(0.2) ⇒ Y = 9000
c) When Y = 9000, consumption equals 1400 + (0.8 × 9000) = 8600. Saving therefore
equals Y – C which is 9000 – 8600 = 400. Investment equals 400.
Question 10
The discussion is best worked out in terms of the figure below, which shows the
equilibrium level of national income in terms of desired saving and desired investment. The
initial equilibrium is point A. The rise in desired saving shifts up the saving function to S′
but does not affect the investment function. The accompanying reduction in desired
consumption leads to an unintended accumulation of inventories and thus leads firms to
reduce the level of output. After the multiplier has worked itself out, the level of
equilibrium income has fallen but the equilibrium level of saving is unchanged. Thus, the
attempt to increase saving leads to a reduction in national income but no increase in overall
saving — the “paradox of thrift.”
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