Keynesian Macromodels 

a. Simple Multiplier  
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 I_{0}. Consumption function: C = C_{0} + cY Demand for consumer goods C is equal to autonomous part C_{0} plus demand proportional to Income Y. C_{0} 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 = C_{0} + cY + I_{0} In macroeconomic equilibrium the income Y must be equal to Aggregate Demand AD. Y = AD and therefore Y = C_{0} + cY + I_{0} 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.  
Now let the parameters of the model have the following numerical values: C_{0} = 50 c = .8 I_{0} = 50 It follows that the multiplier is m = 5 the autonomous expenditure is A = 100 and the equilibrium income is Y_{eq} = 500. It then follows from the consumption function that C = 450 and saving is S = Y_{eq}  C = 50; Note that saving is equal to investment S = I_{0} = 50  
 



