$1.$ Assume that the long$-$run aggregate supply curve is vertical at Y $=3,000$ while the short$-$run aggregate supply curve is horizontal at P $=1\mathrm{.}0.$ The aggregate demand curve is Y $=3($M$/$P$)$ and M $=1,000.$

A$)$ If the economy is initially in long$-$run equilibrium, what are the values of P and Y$?$

B$)$ Now suppose a supply shock moves the short$-$run aggregate supply curve to P $=1\mathrm{.}5.$ What are the new short$-$run P and Y$?$

C$)$ If the aggregate demand curve and long$-$run aggregate supply curve are unchanged, what are the long$-$run equilibrium P and Y after the supply shock?

D$)$ Suppose that after the supply shock the Fed wanted to hold output at its long$-$run level. What level of M would be required? If this level of M were maintained, what would be long$-$run equilibrium P and Y$?$

Use a graph to show your work.