1. Recall that the medium-run equilibrium is represented by the Phillips curve:
ID: 1106082 • Letter: 1
Question
1. Recall that the medium-run equilibrium is represented by the Phillips curve: where we assume that wage setters expect inflation this year to be the same as last year, so that Answer the following questions: a. Modify the Phillips curve to show the relationship between the change in the inflation rate, -(-1), and the output gap, Y-Y, where Y denotes actual output and Y denotes potential output. Hints: You need to re-define the Phillips curve equation using the output gap, Y- instead of the unemployment gap, u - un Derive the level of employment, N, in terms of the rate of unemployment, u Derive the natural level of employment, Nn, in terms of the natural rate of unemployment, un Use N to derive Y; and Nn to derive Y Remember to use the following production function: Y = N, so that Y, Derive the output gap, Y - Ym Substitute u-un to find the Phillips curve expressed in terms of Y- -(-1) b. Given your answer to part (a), what happens to the change in the inflation rate, r(-1), when Y = Y,? C. Given your answer to part (a), what happens to the change in the inflation rate, - t(-1), when Y > Yn? d. Given your answer to part (a), what happens to the change in the inflation rate, - t(-1), when YExplanation / Answer
A)
According to Okun's law, we know that the Rate of Change in Unemployment (Ut - Ut-1)= -A * (Yt-Yt-1)(rate of change of output); where A is some variable
Now, according to the Phillip's Curve argument, Rate of change of inflation = -B * (Ut-Ut-1)rate of change of unemployment; where B is some variable
Now according to the above equations, the Okun's law equation can be substituted in the Phillip's curve equation
Which means, Rate of change of inflation = -B * (-A*rate of change of output)
Thus, Rate of Change of Inflation equals = AB * (Yt-Yt-1)
B)
When Yt = Yn, then Ut - Ut-1 = 0 according to Okun's Law
This further means that according to the Phillips Curve, Rate of change of inflation will also be 0
C)
When Y is greater than Yn, then the rate of unemployment will reduce (according to Okun's Law). This is because negative sign in front of the output variable, thereby showing a decrease in unemployment when the difference between Y and Yn is positive.
When Rate of Unemployment reduces, then employment increases (according to Phillip's Curve). Again, there is a negative sign for the unemployment variable, and thus when unemployment reduces or becomes negative, then inflation increases
D)
When Y is lesser than Yn , then unemployment will increase (according to Okun's law). This is because negative sign in front of the output variable, thereby showing a negative relation between unemployment and output.
When Unemployment increases, then Inflation decreases (according to Phillips Curve). Again, a negative variable for unemployment signifies a negative relation between inflation and unemployment
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