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Ragan/Lipsey 11th Edition
Question 1
a) Public saving is equal to the government budget surplus, which is equal to T–G. If G is
$155 billion for any level of national income, the surplus is straightforward to compute.
The completed table is shown below.
National
Income
(Y)
Net Tax
Revenues
(T)
Public
Saving
(T–G)
100
200
300
400
500
600
700
800
45
70
95
120
145
170
195
220
–110
–85
–60
–35
–10
15
40
65
b) See the diagram below. The public saving function is upward sloping because as
national income rises the government collects more tax revenue and spends less on
transfers. Thus net tax revenue (T) rises for a given amount of government purchases (G).
T – G therefore rises as national income rises.
c) The net tax rate is the amount by which net tax revenues rise in response to a rise in
national income. It is the slope of the public saving function. In this case, each $100
billion increase in real national income leads to a $25 billion increase in net tax revenues.
Thus the net tax rate is 0.25, which is the slope of the T – G function in the figure above
(note that scales on the two axes are different).
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d) The increase in G by $15 billion means that the amount of public saving falls by $15
billion at each level of national income. Thus the public saving function shifts down by
$15 billion.
Question 6
a) Recall that the marginal propensity to spend out of national income is equal to
z = MPC(1–t) – m
The values of z for the various hypothetical economies are:
Economy A:
Economy B:
Economy C:
Economy D:
z = 0.75  (1 – 0.2) – 0.15 = 0.45  Multiplier = 1.82
z = 0.75  (1 – 0.2) – 0.30 = 0.30  Multiplier = 1.42
z = 0.75  (1 – 0.4) – 0.30 = 0.15  Multiplier = 1.17
z = 0.90  (1 – 0.4) – 0.30 = 0.24  Multiplier = 1.32
Recall that the simple multiplier is equal to 1/(1–z).
b) Comparing Economies A and B, we see that the marginal propensity to spend out of
national income is higher in the economy with the lower value of m. A lower marginal
propensity to import means that each $1 increase in national income leads to a smaller
increase in expenditure on imports, and thus a larger increase in expenditure on the output
of domestic producers. Thus, the multiplier will be higher when m is smaller.
c) Comparing Economies B and C, we see that the economy with the lower income-tax rate
has the higher marginal propensity to spend out of national income. Other things equal (like
MPC and m), a lower tax rate means that each $1 increase in national income leads to a
larger increase in disposable income and thus a larger increase in consumption
expenditures. Thus the multiplier is larger when t is smaller.
d) Comparing Economies C and D, we see that the economy with the higher MPC has the
higher marginal propensity to spend out of national income. Other things equal (like t and
m), a higher MPC means that each $1 increase in national income leads to a larger increase
in consumption expenditures. Thus the multiplier is larger when MPC is higher.
Question 8
a) The consumption function is:
C = a + bYD
YD is the difference between national income and total tax revenues:
YD = Y – tY = Y(1 – t)
Putting this expression for YD into the consumption function, we get the relationship
between consumption and national income:
C = a + bY(1 – t )
b) The AE function is:
AE = a + bY(1 – t) + I0 + G0 + (X0 – mY)
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We can collect all of the autonomous terms together, and collect all of the terms in Y
together, to simplify the AE function as:
AE = [a + I0 + G0 + X0] + [b(1 – t) – m]Y
c) The equilibrium condition is Y = AE. Imposing this condition, and using A to be the sum
of all the autonomous terms, we get
Y = A + [b(1 – t) – m]Y
d) The equilibrium value of national income is the value that solves the above equation.
Call this value YE. The solution is
YE = A/(1 – z)
Where z = [b(1 – t) – m] is the marginal propensity to spend out of national income.
e) If the level of autonomous spending increases by A, then the equilibrium level of
national income rises by 1/(1 – z) times A. 1/(1 – z) is the simple multiplier.
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