Keynesian Macro Model II

Aggregate Output equals Aggregate Expenditures in equilibrium

Y = GDP = C + I + G + ( X - M )

Where:

Y is Aggregate Income

GDP = Gross Domestic Product

C = Consumption Expenditures

I = Investment Expenditures

G = Government Expenditures

X = eXports

M = iMports

( X - M ) = Net Exports

T =Taxes =Ywhere tau, , is the tax rate

Yd = Disposable Income = Y - T orYd = Y -YorYd = (1-)Y, where is the tax rate

Let

C = +Yd = 300 + 3/4 Yd

where is called autonomous or "leech" amount of consumption expenditure and is the additional amount of consumption expenditures induced by anadditionalunit of disposable income. This is the Consumption Function.

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Homework

what is beta

What do we call ?

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I = 200 -r where r is the interest rate and is how sensitive investment expenditures are to changes in the interest rate. Note that this relationship is an inverse or negative relationship. Again we will ignore the monetary policy impact on the interest rate for now.

G = 100

and even though we know that as income increases people want to import more, for simplicity let's make X = M so net exports are zero

Therefore

Y = C + I + G + ( X - M )

Y = 300 +Yd +200 + 100 ;= 300 + 3/4Yd +200 + 100

Y =300 +(Y -Y ) +200 + 100

Y -(Y -Y ) = 600

[1 -( 1 - )] Y = 600

Y = 1 /[1 -( 1 - )] 600

for fun, let the tax rate be equal to 20% or 1/5 and = 3/4 then solve for Y...

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Equilibrium Y

What is the equilibrium value for Y?

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The multiplier for this model is:

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multiplier

What is the value of the multiplier?

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As we expand the model, you will see that the value of the multiplier decreases. This does NOT negate the efficacy of fiscal policy.

If an economic system is inside the Production Possibility Frontier, then actual output is less than potential output, and employment is less than full employment. Therefore, the unemployment rate is greater than the natural rate of unemployment and having a budget deficit either by increasing government expenditures: G or decreasing taxes: T has a lower opportunity cost than when at potential output.