An economy has the following equation for the Phillips curve: 1: =E1t0.5(u6) People form their expectations of inflation by ta king a weighted average of the previous two years of ination: E1: = 0.71:-1 + 0.31r_2 Okun's law for this economy is: YN YN = 2.0(u - u\") The economy begins at its natural rate of unemployment with a stable inflation rate of 5 percent. 9' What is the natural rate of unemployment for this economy? b. Graph the short-term tradeoff between ination and unemployment that this economy faces. Label the point where the economy begins as point A. (Be sure to give numerical values for point A.) c. A fall in aggregate demand leads to a recession, causing the unemployment rate to rise 4 percentage points above its natural rate. On your graph in part (a), label the point the economy experiences that year as point 8. (Once again, be sure to give numerical values.) d. Unemployment remains at this high level for two years (the initial year described in part (c) and one more), after which it returns to its natural rate. Create a table showing unemployment, ination, expected ination, and output growth for 10 years beginning two years before the recession. (Feel free but not obligated to use Excel.) e. On the same graph you used in part (b), graph the short-run tradeoff the economy faces at the end of this 10-year period. Label the point where the economy nds itselfas point C. (Again, use numerical values.) f. Compare the equilibrium before the recession with the new long-run (period ten) equilibrium. How many percentage points of output are lost during the transition? What is this economy' 5 sacrice ratio