Question

Derive the aggregate demand curve using both the expenditure function and the MP curve (show these graphic derivations separately). These two derivations give slightly different representations of the AD curve. Explain the difference.

Answer 1

Deriving aggregate demand from total expenditure:

Aggregate demand curve can be derived from the aggregate expenditures curves for different price levels. The equilibrium real GDP associated with each price level in the aggregate expenditures model is plotted as a point showing the price level and the quantity of goods and services demanded (measured as real GDP). At a price level of 1.0, for example, the equilibrium level of real GDP in the aggregate expenditures model in Panel (a) is $6,000 billion at point B. That means $6,000 billion worth of goods and services is demanded; point B' on the aggregate demand curve in Panel (b) corresponds to a real GDP demanded of $6,000 billion and a price level of 1.0. At a price level of 0.5 the equilibrium GDP demanded is $10,000 billion at point C', and at a price level of 1.5 the equilibrium real GDP demanded is $2,000 billion at point A'. The aggregate demand curve thus shows the equilibrium real GDP from the aggregate expenditures model at each price level.

(Source: https://2012books.lardbucket.org/books/macroeconomics-principles-v2.0/s16-03-aggregate-expenditures-and-agg.html)

Deriving aggregate demand from MP Curve:

The MP curve in panel (a) shows that as inflation rises from 1.5% to 2% to 3.0%, the real interest rate rises from 1.5% to 2.0% to 2.5%. The IS curve in panel ( b) then shows that higher real interest rates lead to lower planned investment spending, and hence aggregate output falls from $10.5 trillion to $10 trillion to $9.5 trillion. Finally, panel (c) plots the level of equilibrium output corresponding to each of the three inflation rates: the line that connects these points is the AD curve, and it is downward sloping.  

(Source: https://rudiunpad.files.wordpress.com/2014/03/m23_mish5701_05_se_c23.pdf)

For graph refer attached image,