Department

Economics for Management StudiesCourse Code

MGEA06H3Professor

Iris AuLecture

4This

**preview**shows pages 1-2. to view the full**6 pages of the document.**AGGREGATE EXPENDITURE—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 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?

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 × 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

Canadian goods.

Conclusion: Exports are inversely related to exchange rate:

X = X

0 – x1 (E – ), where X0, x1 & are constants

X

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.

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 × 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.

Note:

* 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,

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 – 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

Æ

5/8 Y = 700

Æ

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*)

National Saving—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 – 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.

S

P = Y – T + TR – C = DI – C

S

G = T – TR – G

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