Chapter 22: Adding Government and Trade to the Simple Macro Model
Question 2
a) Net exports are equal to exports minus imports. If exports are equal to $300 billion for
any level of national income, then net exports are easily computed. The completed table
is shown below.
National
Income (Y)
Imports
(IM)
Net Exports
(X – IM)
100
200
300
400
500
600
700
800
85
120
155
190
225
260
295
330
215
180
145
110
75
40
5
–30
b) See the figure below. The net export function is downward sloping because increases
in real national income lead to increases in imports (IM) but leave exports (X) unchanged.
Thus X – IM falls as real national income rises.
c) The marginal propensity to import is the change in imports that results from a $1
change in national income. From the information provided in the table above, for each
$100 billion increase in national income, imports increase by $35 billion. Thus the
marginal propensity to import is 0.35. This is the (absolute value of the) slope of the net
export function.
d) If one of Canada’s major trading partners experiences a recession, firms and
households in that country will demand fewer Canadian goods and services. This results
in a reduction in Canada’s exports, X. Net exports will decline at any level of Canadian
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national income. Thus the net export function will shift down. For example, a reduction
in Canadian exports of $20 billion would shift the net export function vertically
downward by $20 billion.
Question 4
a) Desired investment (I) is 50, as shown by the height of the line marked I in the figure.
b) Government purchases (G) is 50, shown by the difference between the I and G+I lines in
the figure.
c) The vertical intercept of the AE function is 150. This is all autonomous expenditure,
including consumption, investment, government, and exports. We know that government
and investment sum to 100. We are told that autonomous exports are 25. Thus the level of
autonomous consumption must be 25.
d) Total autonomous expenditure is 150, the vertical intercept of the AE function.
e) A decrease in G by $25 billion will shift the AE function down (in a parallel fashion) by
$25 billion. Equilibrium national income will fall by $25 billion times the simple
multiplier.
f) An increase in the net tax rate shifts the AE function down and also makes it flatter.
Equilibrium national income will fall.
g) An increase in desired investment by $50 billion will shift the AE function up (in a
parallel fashion) by $50 billion. Equilibrium national income will rise by $50 billion times
the simple multiplier.
h) A reduction in the marginal propensity to import will shift the AE function upwards and
also make it steeper. Equilibrium national income will rise.
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
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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)
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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