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MGEA06H3
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Iris Au
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Lecture

# Week4 Lecture

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University of Toronto Scarborough

Economics for Management Studies

MGEA06H3

Iris Au

Winter

Description

1
ECMA06 – Aggregate Expenditure (with government and foreign sector)
Aggregate Expenditure – with Government & Foreign
Sector
Outline
• Extend the simple model developed last week by including
government and foreign sector in the model.
• National saving in an open economy.
• Consider the effects of a change in aggregate expenditure on
national income and budget balance.
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Enriching the Model – Including Government and Foreign Sector
The Government Sector
The government enters the model in the following ways:
1) Collecting taxes, T
• The government collects taxes from households and firms to
finance its spending.
• Assumption: Taxes are positively related to income.
• Tax function:
T = T +0t Y,1 where T = 0utonomous taxes
t1= tax rate & 1 > t > 1.
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
2) Making transfer payments, TR
• Transfer payments refer to payments from the government to
individuals that are not in exchange for goods and services.
• Examples include employment insurances (EI), public
pension, and etc.
• Assumption: Transfer payments are inversely related to
income.
• Transfer payments function:
TR = TR – t0 Y, 1here TR = auton0mous transfer
tr1= benefit reduction rate &
1 > tr > 0
1
3) Spending on final goods and services, G
• It is also called government purchases, and it is the
government expenditure on final goods and services.
• Assumption: G is an autonomous variable, (i.e., its value is
given), i.e.,
G = constant.
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The Foreign Sector
• When an economy trades with foreign countries, this
economy is an open economy.
Exchange Rate
• Exchange rate (E) is the price of a country’s currency in
terms of another currency.
• In our class, exchange rate measures the value of C$ in
foreign currency (i.e., the # of foreign currency needed to
exchange 1 C$).
• Example: If E = US$ 0.875/C$, then the value of 1 C$ is
equivalent to US$ 0.875 (US$ 0.875 per C$).
• Question: What happens when E changes?
• Answer:
⇒ If E ↑, then C$ appreciates against the US$ because it
takes more US$ to exchange 1 C$.
⇒ If E ↓, then C$ depreciates against the US$ because it
takes fewer US$ to exchange 1 C$.
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
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The foreign sector enters the model in the following ways:
1) Exports, X
• Assumption: Exports depend on the exchange rate only.
⇒ When E ↑(i.e., C$ appreciates), X ↓because Canadian
goods become more expensive to foreigners, foreign
demand for Canadian goods ↓ .
• Exports are inversely related to exchange rate.
• Exports function:
X = X –0x (E1– ), where X = 0utonomous exports
x & are constants
1
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
2)Imports, IM
• Assumption: Imports depend on income and exchange rate.
⇒ Holding all else constant, IM ↑when Y ↑because when
Y ↑ , we consume more goods including imported goods
⇒our demand for foreign goods ↑ .
⇒ Holding all else constant, IM ↑ when E ↑ (C$
appreciates) because foreign goods become less
expensive to us, our demand for foreign goods ↑ .
• Imports are positively related to both income and exchange
rate.
• Imports function:
IM = IM + 0m Y +1im (E – 2,
where IM = 0utonomous imports
im 1 = marginal propensity of imports
im 2 are constants
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A More Complicated Model
Suppose the model consists of the following functions:
C = 20 + DI
T = (2/7)Y – 20
TR = 220 – (1/7)Y
I = 100 – 5(r – 0.0r = 0.05
G = 250
X = 120 – 3(E – 0.85); E = 0.85 (US$ 0.85 per C$)
IM = Y + 2.5(E – 0.85); E = 0.85
Note: We have a much more complicated model, but for now we keep it by
holding the interest rate (r) and the exchange rate(E) constant.
Note:
*When T = TR = 0, DI= Y= Y = the marginal propensity to spend out of GDP (= Y)
** When ≠ 0 and ≠R 0, D≠ Y ⇒ ≠ c ≠ MPC. Now = the marginal
Y
propensity to spend out of DI.
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
Solving for Equilibrium
• To solve for the equilibrium, we try to get the AE equation:
AE = AE + c Y,
0 Y
where c Y marginal propensity to consume out of Y
• Steps:
1) Get the consumption function as a function of GDP (Y)
2) Get the AE function by setting AE = C + I + G + X – IM
3) Solve for Y by equating AE = Y.
Step 1: Get C = C(Y)
C = 20 + (7/8)DI, where DI = Y – T + TR
• Get DI:
• Get C = C(Y):
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Step 2: Get the AE Function
AE = C + I + G + X – IM
• Holding r = 0.05 ⇒I = 100 – 5(0.05 – 0.05) = 100
• Holding E = 0.85 ⇒X = 120 – 3(0.85 – 0.85) = 120
⇒IM = Y + 2.5(0.85 – 0.85) = Y
Step 3: Solve for Y
Equilibrium is given by Y = AE.
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
Checking Our Answer (only if asked for)
• We can check our results by finding values for all the variables and check whether they add up
to the equilibrium level of Y.
T: T = (2/7)Y – 20 = (2/7)1120 – 20 =
TR: TR = 220–(1/7)Y = 220–(1/7)1120 =
DI:DI = Y – T + TR =
C: C = 20 + DI =
I: I = 100
G: G = 250 (given)
X: X = 120
IM: IM = Y =
• Now, we can check our results:
Y = C + I + G + X – IM
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National Saving in an Open Economy
• For an open economy:
Y = C + I + G + X – IM
Lessons:
• For an open economy, national saving MUST equal to the
sum of (domestic) investment and net exports, i.e.,
NS = I + NX.
• An open economy can save in 2 ways:
1) Undertaking investment.
2) Running a trade surplus (accumulate foreign wealth)
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
• From last week lecture: NS = S + S .
p
SG= Y – T + TR – C = DI – C
S = T – TR – G
• (Continued from our numerical example on p7) What is the level of private saving?
S = DI – C =
• What is the level of public saving?
G
⇒ If S < 0, then the government runs a budget deficit.
G
⇒ If S > 0, then the government runs a budget surplus.
⇒ If S = 0, then the government runs a balanced budget.
S = T – TR – G =
• What is the level of national saving?
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• What happens to net exports?
⇒ If NX < 0, then the country has a trade deficit.
⇒ If NX > 0, then the country has a trade surplus.
NX = X – IM =
• Check:
Recall, NS = I + NX
• Note: In this example, the country haseficits – the simultaneous occurrence of budget
deficit and trade deficit.
• Over the past few years, the Americans have had very large trade deficits and very large
budget deficits. This is no accident!
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ECMA06 – Aggregate Expenditure (with government and foreign sector)
Effect of a Change in AE on Y
• We will consider what happens when we change one of the parameters of the model.
• Return to our extended model (hold r & E constant):
Generic form Numerical example
C = C +0c DI1 C = 20 + DI
T = T +0t Y1 T = – 20 + (2/7)Y
TR = TR – t0 Y 1 TR = 220 – (1/7)Y
I = I0 I = 100
G G = 250
X = X 0 X = 120
IM = im Y 1 I

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