ECMA06 – Aggregate Expenditure (with government and foreign sect1r)
Aggregate Expenditure (continued) – with Government &
Extend the simple AE model by including government and
foreign sector in the model.
Discuss national saving in an open economy.
Consider the effects of a change in aggregate expenditure on
national income and budget balance. ECMA06 – Aggregate Expenditure (with government and foreign sector2
Enriching the Model – Including Government and Foreign
The Government Sector & The Budget Balance
The government enters the model in the 3 ways:
1)Spending on final goods and services, G
It is the government expenditure on final goods and
Assumption: G is an autonomous variable, (i.e., its value is
given), i.e., G = constant.
2)Collecting taxes, T
Assumption: Taxes are positively related to income because
the government collects taxes from households and firms to
finance its spending.
T = T 0 t 1, where T =0autonomous taxes
1 = tax rate & 1 > t1> 0. ECMA06 – Aggregate Expenditure (with government and foreign sec3or)
3)Making transfer payments, TR
Assumption: Transfer payments are inversely related to
They are payments from the government to individuals that
are NOT in exchange for goods and services.
Examples include employment insurances (EI), public
pension, and etc.
Transfer payments function:
TR = TR – tr Y, where TR = autonomous transfer
0 1 0
tr = benefit reduction rate &
1 > tr > 0
Budget Balance & Public Saving
Budget balance (BB) = T – TR – G
If S < 0, then the government runs a budget deficit.
If S > 0, then the government runs a budget surplus.
If S = 0, then the government runs a balanced budget.
* The budget balance is just the same as public saving (S ) ECMA06 – Aggregate Expenditure (with government and foreign s4ctor)
The Foreign Sector & the Trade Balance
When an economy trades with foreign countries, this
economy is an open economy.
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$).
Question: What happens when E changes?
If E , then C$ 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$. ECMA06 – Aggregate Expenditure (with government and foreign sec5or)
The foreign sector enters the model in the following ways:
Assumption: Exports depend on the exchange rate only and are
inversely related to exchange rate.
When E (i.e., C$ appreciates), X because Canadian
goods become more expensive to foreigners, foreign
demand for Canadian goods .
X = X 0 x 1E – E ), where X =0autonomous exports
x 1 E are constants ECMA06 – Aggregate Expenditure (with government and foreign6sector)
Assumption: Imports are positively related to income and
Holding all else constant, we consume more goods
including imported goods when Y IM .
Holding all else constant, foreign goods become less
expensive to us when E (C$ appreciates), our
demand for foreign goods IM .
IM = IM +0im Y1+ im (E2– E),
where IM =0autonomous imports
im 1 IM = marginal propensity of imports
im 2 E are constants
Trade Balance = NX = X – IM
If NX < 0, then the country has a trade deficit.
If NX > 0, then the country has a trade surplus. ECMA06 – Aggregate Expenditure (with government and for7ign sector)
A More Complicated Model – Including All Sectors
Suppose the model consists of the following functions:
C = 20 +⅞ DI
T = (2/7)Y – 20
TR = 220 – (1/7)Y
I = 100 – 5(r – 0.05); r = 0.05
G = 250
X = 120 – 3(E – 0.85); E = 0.85 (US$ 0.85 per C$)
IM = ⅛Y + 2.5(E – 0.85); E = 0.85
Note: For now to keep the model RELATIVELY simple, we
hold the interest rate (r) and the exchange rate(E) constant.
*Last week, when T = TR = 0, DI = Y c = c = the
marginal propensity to spend out of GDP (= Y)
** Now, T 0 and TR 0, DI Y c1 cY. ECMA06 – Aggregate Expenditure (with government and foreign8sector)
Solving for Equilibrium
To solve for the equilibrium, we try to get the AE equation:
AE = AE +0c YY
where cY= marginal propensity to consume out of Y
1)Get the consumption function as a function of 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 + ⅞ DI, where DI = Y – T + TR
Get C = C(Y): ECMA06 – Aggregate Expenditure (with government and foreign secto9)
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 = ⅛Y + 2.5(0.85 – 0.85) = ⅛Y
Step 3: Solve for Y
Equilibrium is given by Y = AE. ECMA06 – Aggregate Expenditure (with government and forei10 sector)
Checking Our Answer
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 + ⅞ DI =
I: I = 100
G: G = 250 (given)
X: X = 120
IM: IM = ⅛Y =
Now, we can check our results:
Y = C + I + G + X – IM ECMA06 – Aggregate Expenditure (with government and foreign se11or)
National Saving in an Open Economy
For an open economy:
Y = C + I + G + X – IM
Y – C – G = I + (X – IM)
Y – C – G = I + NX
For an open economy, national saving MUST equal to the
sum of (domestic) investment and net exports.
An open economy can save in 2 ways:
1) Undertaking investment.
2) Running a trade surplus (accumulate foreign wealth) ECMA06 – Aggregate Expenditure (with government and foreign se12or)
(Continued from our numerical example on p7). Find the
levels of private saving, public saving, national saving, and net
S = DI – C
S = T – TR – G
National saving, NS
NS = S + S
NX = X – IM
Recall, NS = I + NX
Note: In this example, the country has twin deficits – the
simultaneous occurrence of budget deficit and trade deficit. ECMA06 – Aggregate Expenditure (with government and foreign secto13
Effect of a Change in Autonomous AE (AE ) on Y 0
Our extended model (IM = 00 and hold r & E constant):
Generic form Numerical example
C = C + c DI