# Lecture notes from week 4

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30 Nov 2010
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AGGREGATE EXPENDITUREβINCLUDING GOVERNMENT & FOREIGN SECTOR
Outline
x We complicate the simple model developed last week and we include government and foreign sector in the model.
x National savingβrevisit.
x Consider the effects of a change in aggregate expenditure on national income and budget balance.
Enriching the Modelβ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 β 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 countryβ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?
x Answer:
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.
Example
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 Γ 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 Γ 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
Canadian goods.
Conclusion: Exports are inversely related to exchange rate:
X = X
0 β x1 (E β ξ), where X0, x1 & ξ are constants
X
0 = autonomous exports, x1 is amount that exports will decrease by if E > ξ
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 Γ 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.
Example
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 Γ 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 Γ 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 β ξ), where IM0, im1, im2 & ξ are constants
IM0 = autonomous imports, im1 = marginal propensity to import (1 > im1 > 0), im2 is amount that imports increase by if E > ξ
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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 β 20
TR = 220 β (1/7) Y
I = 100 β 5 (r β 0.05); r = 0.05
G = 250
X = 120 β 3 (E β 0.85); E = 0.85 (US\$ 0.85 per C\$)
IM = 1/8 Y + 2.5 (E β 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.
Note:
* When T = TR = 0, DI = Y Γ 7/8 = cY = the marginal propensity to spend out of GDP (= Y)
** When T ξ 0 and TR ξ 0, DI ξ Y Γ 7/8 ξ cY ξ 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,
c
Y = marginal propensity to consume out of Y
x Steps:
1) Get the consumption function as a function of GDP (Y)
2) Get the AE function by setting AE = C + I + G + X β IM
3) Solve for Y by equating AE = Y
Step 1: Get C = C (Y)
C = 20 + (7/8) DI, where DI = Y β T + TR
x Get DI:
DI = Y β T + TR = Y β [(2/7) Y β 20] + [220 β (1/7) Y] = (4/7) Y + 240
x Get C = C (Y):
C = 20 + (7/8) [240 + (4/7) Y = 20 + 210 + Β½ Y = 230 + Β½ Y
C (Y) = 230 + Β½ Y
Step 2: Get the AE Function
*** AE = C + I + G + X β IM ***
x Holding r = 0.05 Γ I = 100 β 5 (0.05 β 0.05) = 100
x Holding E = 0.85 Γ X = 120 β 3 (0.85 β 0.85) = 120
Γ IM = 1/8 Y + 2.5 (0.85 β 0.85) = 1/8 Y
AE = C + I + G + X β IM = (230 + Β½ Y) + 100 + 250 + 120 β 1/8 Y = 3/8 Y + 700
AE = 700 + 3/8 Y
Step 3: Solving for Y
Y = AE
Y = 700 + 3/8 Y
Γ
5/8 Y = 700
Γ
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 β 20 = (2/7) 1120 β 20 = 300
TR: TR = 220 β (1/7) Y = 220 β (1/7) 1120 = 60
DI: DI = Y β T + TR = 1120 β 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 β IM
Y = C + I + G + X β IM = 790 + 100 + 250 + 120 β 140 = 1120 (same as Y*)
National SavingβRevisit
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?
x Answer:
Y = C + I + G + X β IM
Y β C β G = I + X β IM Γ NS = I + NX as NS = Y β C β G and NX = X β 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.
S
P = Y β T + TR β C = DI β C
S
G = T β TR β G
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## Document Summary

N we complicate the simple model developed last week and we include government and foreign sector in the model. N consider the effects of a change in aggregate expenditure on national income and budget balance. The government enters the model in the following ways: collecting taxes, t. The government collects taxes from households and firms to finance its spending. In our model taxes are positively related to income, i. e. , where t0 = constant, 1 > t1 > 0. T = t0 + t1y: 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 insurance (ei), public pension, and etc. Transfer payments are inversely related to income, i. e. , where tr0 = constant, 1 > tr1 > 0. It is also called government purchases, and it is the government expenditure on final goods and services.

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