Phillips Curve. An economy has the following functions for its short run aggregate supply (SRAS), Okun's Law (OL), and Phillips Curve (PC): SRAS: P = EP + (1/2)(Y - 3) OL: (Y - Y) = -4(u - un) PC: It = En - (1/5) (u - 6) The economy begins at its natural rate of output with a stable price level equal to $5. a.) Output is at its natural level when the price level is equal to expectations. Calculate the natural rate of output in this economy. b.) Construct a graph containing an aggregate demand curve, a short-run aggregate supply curve, and a long-run aggregate supply curve. Indicate the values of Y and P at the short-run equilibrium. Be sure to label the x- and y-axes. c.) Unemployment is at its natural rate when inflation is equal to its expectations. Calculate the natural rate of unemployment in this economy. d.) Assume in equilibrium this economy has a stable inflation rate of 20%. Graph the short-run tradeoff between inflation and unemployment that this economy faces and label the inflation and unemployment values of the equilibrium point on the yand x-axis respectively. e.) Suppose the central bank unexpectedly expands the money supply and there is an unexpected rise in the price level from $5 to $7. Assume that expectations of the price level are equal to the level of the previous period. Calculate the rate of output Y in the short run. Show the effect of such an event on your graph and label the new equilibrium values for Y and P f.) Using the rate of output calculated in part e.), use the Okun's Law equation to calculate the short-run unemployment rate. What happened to unemployment as a result of the unexpected increase in price level? g.) Using the numbers for the price level, calculate the inflation rate after the expansionary monetary policy (Hint: n = P-P-1). P-1 "Then, use the Phillips Curve equation to calculate the short-run unemployment rate (use decimal values for inflation- i.e. use .20 not 20%). How does this compare with the unemployment rate you calculated in part f.)? Show the new short-run equilibrium on your Phillips Curve graph. h.) In the long run, the public expects a higher price level and higher inflation. Show the impact of these adjusted expectations in your graphs from part b.) and your Phillips Curve graph. Be sure to label the appropriate values on the y- and x-axes for both graphs (except for the price level in the graph from part b.), which we didn't define)