a. Write down an equation for the Phillips Curve b. Explain in words the relationship between expected future inflation and current inflation and the relationship between the unemployment gap and current inflation that the Phillips Curve implies. c. Suppose that in late 2029 you estimate the slope of the Phillips curve (a) coefficient by using the historical inflation and unemployment data from 2024 through 2029. Your analysis of the data leads you to believe that a = 0.5. Suppose you also judged that U* = 4% and that 1 = 2%. Over the 2024-2029 period swings for U and I have been modest and the Phillips curve has been a successful tool for predicting inflation. In 2030, however, unemployment soars, equaling 16% for the year. You exercise your Phillips curve model. What does it predict for inflation in 2030? d. In 2030, the actual inflation rate turns out to be 0.8%. What would be the parameter value for a that correctly predicted 2030 inflation, using a standard Phillips curve? e. If you use your new value for a, it correctly predicts 2030, but does a poor job in previous years. Draw the Phillips curve, using your Phillips curve equation and the original value you estimated for a. On the same graph, draw a Phillips curve that can accommodate the 2024-2029 period and the 2030 period. (Draw a PC that makes sense in light of the discussion and the value of a) f. What real world forces explain why the Phillips curve might look like the second curve that you drew? g. Explain why the standard Phillips curve equation cannot accommodate the second graph you drew.