Show the equations of the as-ad model, Macroeconomics

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Q. Show the equations of the AS-AD model?

The equations of the AS-AD model

To précis the AS-AD model, we can have a glance at its equations. IS-LM model was "solved" by simultaneously solving below equations 

YD(Y, R) = Y

MD(Y, R) = MS

For Y and R. As MS was exogenous, we had two equations and two unknown and system of equation could be solved. Solution was explained by IS-LM diagram. 

In AS-AD model, situation is slightly more complicated since MD now relies on three variables: Y, R and P. We can no longer solve 

YD(Y, R) = Y

MD(Y, R, P) = MS

For Y, R and P as we have three unknowns and only two equations. We need one more equation in AS-AD model. The third equation in AS-AD model comes from the production function and the labor market. We illustrated that L depends on P and as YSrelies on L, YS will depend on P. Equilibrium requires that their supply equals actual production which is YS (P) = Y. The three equations of AS-AD model are thus:

YD(Y, R) = Y

MD(Y, R, P) = MS

YS (P) = Y

These are to be solved for Y, R and P. Solution is explained in AS-AD diagram, where first two equations are summarized in AD curve YD (P) = Y.

Note how the three different versions of Keynesian model are related to the number of variables / equations. 

  • In cross model, we have only one variable (Y) and an equation: YD(Y) = Y.
  • In IS-LM model, we have two variables (Y and R) and two equations: YD(Y, R) = Y and MD(Y, R, P) = MS.
  • In the AS-AD model, we have three variables (Y, R, P) and three equations: YD(Y, R) = Y, MD(Y, R, P) = MSoch YS (P) = Y.

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