# MGEA06H3 Lecture Notes - Lecture 3: Shortage, Autarky

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30 Nov 2010
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AGGREGATE EXPENDITURE—THE SIMPLEST SHORT-RUN MODEL
Outline
x Build a simple model that determines equilibrium national income.
x Simple model consists of consumption and investment only (will take into account of government and foreign sector next week).
x Consider how does a change in aggregate expenditure affect national income (we will also discuss the multiplier).
Why Do We Want to Develop a Model That Determines National Income?
x Question: Does demand (planned expenditure) always equal to supply (actual expenditure)?
x Answer: Not necessary! But why?
o Supply = actual expenditure = actual national income: GDE = C + I + G + X – IM
o Demand (AD) = desired expenditure: AD = C + I + G + X – IM except unexpected changes in inventories.
o The key is investment (I) in GDE includes unintended change in inventories while investment (I) in AD includes only
intended investment.
x It is certainly true that every act of production generates income for Canadians; however, not all of that income gets translated into
demand for the output of firms.
x We want a model that has some positive relationship between
The income generated by production
and
The demand that exists for that production
Model of the Macro Economy
x The underlying model is given by:
AE = AE0 + cY
where AE = aggregate expenditure = aggregate demand
AE0 = autonomous expenditure = constant
c
Y = d AE / d Y = constant, 0 < cY < 1
Y = GDP = output = income
Y
x cY basically says that every time income increases by \$1 that amount will be divided between spending and saving. cY is the amount
that will be spent. So, if cY is 0.85, then 85 cents will be spent for every \$1 increase in income.
x In Canada, the cY rate is about 0.7 right now. This means that for every \$1 income, 70 cents are spent for consumption.
x We will start with a simple model first so that you have a feel what the model looks like.
x When we make the model more detailed later on, we will have:
** AE = C + I + G+ X – IM **
x FOR NOW, we assume I, G, and X are exogenous variables.
o Exogenous variables—these are given to the model (i.e., they are constants and you do not need to solve for them). However,
external factors can change the values of these variables.
x FOR NOW, we assume C and IM are endogenous variables.
o Endogenous variables—the values are determined within the model (i.e., you need to solve for them).
x In particular, C and IM as Y (income) changes.
o C and IM are positively related to income.
o If income increases, then consumption (C) increases, and imports (IM) also increase.
Solving for Equilibrium
x We know AE = AE0 + cYY
x AE0 is always a positive number, even if income is 0.
x Question: What level of Y gives us the equilibrium?
x Answer: The equilibrium level of Y, Y*, is the level of Y that generates enough AE to buy itself.
*** Equilibrium: supply = demand Æ Y = AE Æ Y = AE0 + cYY Æ (1 – cY) Y = AE0 Æ Y* = AE0 / (1 – cY)
Example
Suppose AE = 100 + 2/3Y. Find the equilibrium level of Y.
100 = AE0, 2/3 = cY
Equilibrium: Y = AE
Æ
Y = 100 + 2/3Y
Æ
1/3Y = 100
Æ
Y* = 300
In this economy, the equilibrium level of output or the equilibrium level of income is equal to 300.
Building the Model
x Question: Where does this kind of model come from?
o No government: Taxes (T) = 0
Transfer (TR) = 0
Government spending (G) = 0
Transfer—CPP, EI, Child Care Benefit, so on (negative tax—something government pays people)
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o Closed economy (no foreign sector):
Exports (X) = 0
Imports (IM) = 0
AE = C + I + G + (X – IM) = C + I + 0 + (0 – 0) Æ AE = C + I for now
Consumption Function
x A single consumption function:
C = C (DI), where DI = disposable income = Y – T + TR
C = C0 + C1DI, where C0 = autonomous consumption
C1 = marginal propensity to consumer out of DI = MPC
x Consumption is positively related to DI, and consumers spend a fraction of their DI on final goods and services.
x This means that if disposable income increases, then consumption increases and 0 < C1 = MPC < 1.
x Note: If T = 0 & TR = 0 (no government), then DI = Y.
Investment Function
x A simple investment function:
I = I (r), where r = real interest rate
I = I0 dr, where I0 = autonomous investment
d = ûI / ûr = constant
x Investment is inversely related to the interest rate. Why?
x If interest rate increases by a little, then investment will be go down by d amount.
x Answer: We assume firms borrow to finance investments and the interest rate is the cost of borrowing.
x Because when the r increases, the cost of borrowing increases. This tells us that undertaking the investment becomes less profitable,
and therefore investment decreases.
Example
I = 90 – 3 (r – 0.06), where r = 0.06 (6%)
90 represents autonomous investment, and 3 represents d.
I = 90 – 3 (0.06 – 0.06) = 90
If prevailing interest rate is 6% and level of investment can be described by above function, then the level of investment is 90.
x In the meantime, we will assume r is fixed to keep our model simple! We will relax this assumption several weeks later.
Example
Suppose C = 10 + 2/3DI, where DI = Y – T + TR
I = 90 – 3 (r – 0.06), r = 0.06
Solve for the equilibrium level of output for a closed economy (X = 0, IM = 0) with no government (T = 0, TR = 0, G = 0).
x Get the AE equation: AE = C + I + G + X – IM
X = 0, IM = 0, G = 0
AE = (10 + 2/3DI) + (90 – 3 (0.06 – 0.06))
With no government, T = TR = 0
Æ
DI = Y
AE = 10 + 2/3Y + 90 = 100 + 2/3Y
x Solving for Y:
*** Equilibrium: Y = AE
Y =100 + 2/3Y
Æ
Y* = 300
So, equilibrium level of income in this economy is 300.
x Graphically (Keynesian Cross Diagram)
Adjustment Mechanism—How Does the Economy End Up in its Equilibrium
x In this section, we will discuss the adjustment mechanism, i.e., what happens in economy if initial level of Y does not equal to Y*.
x In here we will show that the equilibrium is a stable equilibrium Æ the initial level of Y does not matter, the economy will adjust
itself so that Y will equal Y*.
x Recall, the model does not include government (T = TR = G = 0) and foreign sector (X = IM = 0):
C = 10 + 2/3Y
I = 90 – 3 (r – 0.06), r = 0.06 Æ I = 90 (constant)
AE = C + I = 100 + 2/3Y
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