Q$1.$ Phillip's Curve: For each of the following draw an AD$-$AS diagram and a corresponding Phillip's curve assuming the following: $(1)$ actual RGDP is $$9,200(2)$ full employment RGDP is $$10,000(3)$ the natural rate of unemployment is $5\%$; $(4)$ actual unemployment fluctuates around $5\%$

a$.$ Show in both diagrams the effect of an increase in government purchases that pushes actual RGDP up to full employment

b$.$ Again assume actual GDP is at $$9,200,$ show in both diagrams the effect of the Federal Reserve bank selling versus buying treasury bonds to banks.

c$.$ Again assume actual GDP is at $$9,200,$ show in both diagrams the effect of self$-$correction mechanism.