3. Suppose that the Phillips curve is given by: t = + a-but, where is...

 

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3. Suppose that the Phillips curve is given by: πt = ₁ + a-but, where is the inflation rate, is the expected inflation, u, is the rate of unemployment and, a and b are two positive parameters. Suppose that a fraction λ = [0, 1) of wage contracts are indexed to inflation and = AT₂ + (1-X) πt-1. (a) Derive the new equation for the Phillips curve. [2 marks] (b) Derive an algebraic expression for the natural rate of unemploy- ment, Un [2 marks] (c) The following is an estimated Phillips curve for Canada based on data for 1970-2002: t-t-1 =3.2% - 0.4u. Plot this curve on a graph with us on 2-axis and t-t-1 on y-axis. [2 marks] (d) Assume that the Phillips curve in part (c) is the estimated version of the new Phillips curve that you derived in part (a). Also assume that A=0.5. Find the numerical values of paramters a and b as implied by the estimated Phillips curve. What is the natural rate of unemployment? [4 marks] 3. Suppose that the Phillips curve is given by: πt = ₁ + a-but, where is the inflation rate, is the expected inflation, u, is the rate of unemployment and, a and b are two positive parameters. Suppose that a fraction λ = [0, 1) of wage contracts are indexed to inflation and = AT₂ + (1-X) πt-1. (a) Derive the new equation for the Phillips curve. [2 marks] (b) Derive an algebraic expression for the natural rate of unemploy- ment, Un [2 marks] (c) The following is an estimated Phillips curve for Canada based on data for 1970-2002: t-t-1 =3.2% - 0.4u. Plot this curve on a graph with us on 2-axis and t-t-1 on y-axis. [2 marks] (d) Assume that the Phillips curve in part (c) is the estimated version of the new Phillips curve that you derived in part (a). Also assume that A=0.5. Find the numerical values of paramters a and b as implied by the estimated Phillips curve. What is the natural rate of unemployment? [4 marks]

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a To derive the new equation for the Phillips curve we substitute the expression for expected inflation pite into the original Phillips curve equation ... View the full answer