Department

Economics for Management Studies

Course Code

MGEA06H3

Professor

Iris Au

AGGREGATE EXPENDITUREâ€”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 Discuss the adjustment mechanism.

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 â€“ IM

o Demand (AD) = desired expenditure: AD = C + I + G + X â€“ 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.

Start with a Simple Macro Model

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 â€“ IM **

x FOR NOW, we assume I, G, and X are exogenous variables.

o Exogenous variablesâ€”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 variablesâ€”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 Ã† Y = AE Ã† Y = AE0 + cYY Ã† (1 â€“ cY) Y = AE0 Ã† Y* = AE0 / (1 â€“ cY)

Example

Suppose AE = 100 + 2/3Y. Find the equilibrium level of Y.

100 = AE0, 2/3 = cY

Equilibrium: Y = AE

Ã†

Y = 100 + 2/3Y

Ã†

1/3Y = 100

Ã†

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?

x Start with a simple world

o No government: Taxes (T) = 0

Transfer (TR) = 0

Government spending (G) = 0

î‚ƒ Transferâ€”CPP, EI, Child Care Benefit, so on (negative taxâ€”something government pays people)

www.notesolution.com

o Closed economy (no foreign sector):

Exports (X) = 0

Imports (IM) = 0

AE = C + I + G + (X â€“ IM) = C + I + 0 + (0 â€“ 0) Ã† AE = C + I for now

Consumption Function

x A single consumption function:

C = C (DI), where DI = disposable income = Y â€“ 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 â€“ dr, where I0 = autonomous investment

d = Ã»I / Ã»r = 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 â€“ 3 (r â€“ 0.06), where r = 0.06 (6%)

90 represents autonomous investment, and 3 represents d.

I = 90 â€“ 3 (0.06 â€“ 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 â€“ T + TR

I = 90 â€“ 3 (r â€“ 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 â€“ IM

X = 0, IM = 0, G = 0

AE = (10 + 2/3DI) + (90 â€“ 3 (0.06 â€“ 0.06))

With no government, T = TR = 0

Ã†

DI = Y

AE = 10 + 2/3Y + 90 = 100 + 2/3Y

x Solving for Y:

*** Equilibrium: Y = AE

Y =100 + 2/3Y

Ã†

Y* = 300

So, equilibrium level of income in this economy is 300.

x Graphically (Keynesian Cross Diagram)

Adjustment Mechanismâ€”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 Ã† 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 â€“ 3 (r â€“ 0.06), r = 0.06 Ã† I = 90 (constant)

AE = C + I = 100 + 2/3Y

www.notesolution.com

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