Q$2.(20)$ Phillip's Curve and AD$-$AS Model: Use assumptions below to set up an initial point denoted as the point A for a and b$.$ For each of the following draw an AD$/$AS diagram and a corresponding Phillip's curve assuming the following:

$(1)$ Natural unemployment is $5\%$

$(2)$ Unemployment is $4\%$

$(3)$ Actual GDP is $25,000$

$(4)$ Full employment GDP is $15,000$

Based on the Rational Expectations: Keynesian economists thought of the Phillips curve as a "trade$-$off." They thought policy makers had the ability to pick low unemployment and high inflation or high unemployment with low inflation, or combination in between and that the economy would stay in whatever position they chose. Explain why this view was mistaken based upon the following events. PLEASE SET UP THE INITIAL EQUILIBRIUM POINT FOR AD$-$AS Model and Phillip's Curve Model.

a$.$ Show in both diagrams the effect of a surprise decrease in inflation.

b$.$ Show in both diagram the effect of Friedman and the Natural Rate Theory $($Hint: Using monetary policy in the short run, but self$-$correction in the long run$)$