MONEY and BANKING Lecture NOTES MULTIPLIERS FULL GRAPHICS

Keynesian Macromodels

a. Simple Multiplier

explanation     

numeric example

graphic solution

EXPLANATION

 

Aggregate Demand Identity:

AD = C + I 

Aggregate demand AD is equal to demand for consumer goods C plus demand for investment goods I that will be assumed to be equal to a constant I0.

 Consumption function:

C = C0 + cY   

Demand  for consumer goods C  is equal to  autonomous part  C0  plus demand proportional to Income Y.       C0   and  c  are given parameters. 

In the Consumption function Y is an independent variable, while C depends on Y. Aggregate demand AD depends directly on C and therefore indirectly on Y. Substituting Consumption function for C makes AD directly dependent on Y.

AD = C + I  = C0 + cY + I0

In macroeconomic equilibrium  the income Y must be equal to Aggregate Demand AD.

Y = AD

and  therefore

Y = C0 + cY + I0

so that the equilibrium level of Income Y is obtain by solving the above equation to get

which can be also written as

where  m   is the multiplier and  A is autonomous expenditure.

NUMERIC EXAMPLE

Now let the parameters of the model have the following numerical values:

C0 =  50    c = .8    I0 = 50

It follows that the multiplier  is      m = 5 

the autonomous expenditure is       A = 100

and the equilibrium income is     Yeq =  500.

It then follows from the consumption function that       C = 450

and saving  is       S =  Yeq - C = 50;     

Note that  saving is equal to investment      S = I0 = 50

GRAPHIC SOLUTION

 

 

 

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