Macro Models

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Macro Models
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The Simplest Model
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Circular Flow
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Aggregate Demand and Output
Let C be consumption and I planned investment.
Aggregate demand, AD, is the sum of consumption
and investment,
ADCI.
Let Y denote production or output,
By definition Y-CS,
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Equilibrium
Equilibrium in the goods market
YAD.
Firms undertake planned investment in
anticipation of what consumers will buy, but if
they mis-estimate demand, unsold goods accumulate
as inventory investment I
Y-ADIU
Equilibrium then occurs where
SI
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Says Law
How can savings equal investment in an economy as
complex as our. Do firms and consumers sit down
and decide how much to save and invest? This
overlooks that buyers and sellers are distinct.
Keynes realized that the planned spending of
households might not match the planned production
of firms. This refuted Say's Law which says
that output will give rise to its own demand.
Consumers may save too little or too much and
lead to disequilibrium.
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Algebraic Economy
Consumption function
where C- is autonomous (exogenous) consumption,
and 0ltclt1, the marginal propensity to consume
Savings function
Investment demand
Equilibrium
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Keynesian Cross
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The Multiplier
When we increase autonomous demands, equilibrium
income often rises by more than the initial
increase. We define the ratio of these two the
multiplier,
The exact value of the multiplier will depend
upon the structure of the economy
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The Multiplier - Graphical
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The Math behind the Multiplier
The reason for this is the induced increases in
expenditure, cY. Suppose we increase A by 5, we
get successive rounds of spending,
For values of clt1, this is a bounded geometric
sequence whose value equals 5/(1-c). This is just
the same quantity we would find algebraically as
above when we solved for Y..
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Numerical Example
You are given consumption and investment demands
Form the aggregate demand function
Set YAD
Completing the algebra
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Multiplier Numerical Example
To see the multiplier in action, now increase
investment by 5 units, to I25,
AD50250.75Y
Resolve for equilibrium
YAD750.75Y, Y 300
What is the multiplier