Lecture notes from week 4
DepartmentEconomics for Management Studies
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AGGREGATE EXPENDITURE—INCLUDING GOVERNMENT & FOREIGN SECTOR
x We complicate the simple model developed last week and we include government and foreign sector in the model.
x National saving—revisit.
x Consider the effects of a change in aggregate expenditure on national income and budget balance.
Enriching the Model—Including Government & Foreign Sector
The Government Sector
The government enters the model in the following ways:
1) Collecting taxes, T
x The government collects taxes from households and firms to finance its spending.
x In our model taxes are positively related to income, i.e.,
T = T0 + t1Y, where T0 = constant, 1 > t1 > 0
2) Making transfer payments, TR
x Transfer payments refer to payments from the government to individuals that are not in exchange for goods and services.
x Examples include employment insurance (EI), public pension, and etc.
x Transfer payments are inversely related to income, i.e.,
TR = TR0 – tr1Y, where TR0 = constant, 1 > tr1 > 0
3) Spending on final goods and services, G
x It is also called government purchases, and it is the government expenditure on final goods and services.
x In our model, we assume G is an autonomous variable, (i.e., its value is give), i.e., G = constant.
The Foreign Sector
x When an economy trades with foreign countries, this economy is an open economy.
x Before we discuss how the foreign sector enters the model, we need to talk about the exchange rate.
x Question: What is the exchange rate?
x Answer: Exchange rate (E) is the price of a country’s currency in terms of another currency.
o In our class, exchange rate measures value of C$ in foreign currency (i.e., # of foreign currency needed to exchange 1 C$).
o Example: If E = US$ 0.875/C$, then the value of 1 C$ is equivalent to US$ 0.875 (US$ 0.875 per C$).
x Question: What happens when E changes?
o If E increases from US$0.875/C$ to US$0.89/C$, C$ appreciates against US$ because it takes more US$ to exchange 1 C$.
o If E decreases from US$0.875/C$ to US$0.86/C$, C$ depreciates against US$ because it takes fewer US$ to exchange 1 C$.
The foreign sector enters the model in the following ways:
1) Exports, X
x Holding all else constant, X decreases when E increases (C$ appreciates).
o Canadian goods become more expensive to foreigners, foreign demand for Canadian goods decreases.
Suppose a Canadian product sells for C$200 in Canada.
x If E = 0.85 (US$0.85 = C$1), what is the US$ price of that product?
US$ price of the product = C$ 200 × US$ 0.85 / C$ 1 = US$ 170
x If E increases to 0.9 (US$0.9 = C$1), what is the US$ price of that product?
US$ price of the product = C$ 200 × US$ 0.9 / C$ 1 = US$ 180
x Note: Since the US$ price of the Canadian product rises; Canadian goods become more expensive to Americans. They will buy less
Conclusion: Exports are inversely related to exchange rate:
X = X
0 – x1 (E – ), where X0, x1 & are constants
0 = autonomous exports, x1 is amount that exports will decrease by if E >
2) Imports, IM
x Holding all else constant, IM increases when Y increases.
o When Y increases, we consume more goods and services and some of the goods and services we consumed are imported
goods Æ our demand for foreign goods increases.
x Holding all else constant, IM increases when E increases (C$ appreciates).
o Foreign goods become less expensive to us, our demand for foreign goods increases.
Suppose an American product sells for US$100 in the US.
x If E = 0.85 (US$0.85 = C$1), what is the C$ price of that product?
C$ price of the product = US$ 100 × CS$ 1 / US$ 0.85 = C$ 117.65
x If E increases to 0.9 (US$0.9 = C$1), what is the C$ price of that product?
C$ price of the product = US$ 100 × CS $1 / US$ 0.9 = C$ 111.11
x Note: Since C$ price of the US product falls; the US good become less expensive to Canadians. We will buy more American goods.
Conclusion: Imports are positively related to both income and exchange rate:
IM = IM0 + im1Y + im2 (E – ), where IM0, im1, im2 & are constants
IM0 = autonomous imports, im1 = marginal propensity to import (1 > im1 > 0), im2 is amount that imports increase by if E >
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A More Complicated Model
Suppose the model consists of the following functions:
C = 20 + 7/8 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 = 1/8 Y + 2.5 (E – 0.85); E = 0.85
Note: We have a much more complicated model, but for now we keep it RELATIVELY simple by holding the interest rate (r) and the
exchange rate (E) constant.
* When T = TR = 0, DI = Y Æ 7/8 = cY = the marginal propensity to spend out of GDP (= Y)
** When T 0 and TR 0, DI Y Æ 7/8 cY MPC. Now, 7/8 = the marginal propensity to spend out of DI.
Solving for Equilibrium
x To solve for the equilibrium, we try to get the AE equation:
AE = AE0 + cYY,
Y = marginal propensity to consume out of Y
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
x Get DI:
DI = Y – T + TR = Y – [(2/7) Y – 20] + [220 – (1/7) Y] = (4/7) Y + 240
x Get C = C (Y):
C = 20 + (7/8) [240 + (4/7) Y = 20 + 210 + ½ Y = 230 + ½ Y
C (Y) = 230 + ½ Y
Step 2: Get the AE Function
*** AE = C + I + G + X – IM ***
x Holding r = 0.05 Æ I = 100 – 5 (0.05 – 0.05) = 100
x Holding E = 0.85 Æ X = 120 – 3 (0.85 – 0.85) = 120
Æ IM = 1/8 Y + 2.5 (0.85 – 0.85) = 1/8 Y
AE = C + I + G + X – IM = (230 + ½ Y) + 100 + 250 + 120 – 1/8 Y = 3/8 Y + 700
AE = 700 + 3/8 Y
Step 3: Solving for Y
Y = AE
Y = 700 + 3/8 Y
5/8 Y = 700
Y* = 1120
Checking Our Answer (only if asked for)
x 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 = 300
TR: TR = 220 – (1/7) Y = 220 – (1/7) 1120 = 60
DI: DI = Y – T + TR = 1120 – 300 + 60 = 880
C: C = 20 + 7/8 DI = 20 + 7/8 (880) = 790
I: I = 100
G: G = 250 (given)
X: X = 120
IM: IM = 1/8 Y = 1/8 (1120) = 140
x Now, we can check our results:
Y = C + I + G + X – IM
Y = C + I + G + X – IM = 790 + 100 + 250 + 120 – 140 = 1120 (same as Y*)
x With no government and foreign sector in our model, national saving (NS) = private saving (SP) = investment (I).
x Question: What is the relationship between NS and I if the economy is an open economy and there is a government?
Y = C + I + G + X – IM
Y – C – G = I + X – IM Æ NS = I + NX as NS = Y – C – G and NX = X – IM
o IMPORTANT: For an open economy, the national savings of the economy MUST be equal to the sum of (domestic)
investment and net exports.
x Last week, we know that NS = SG + SP.
P = Y – T + TR – C = DI – C
G = T – TR – G
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