Given a loss function of the form: V = [u+1 − Un]² + d(πt+2 − π¹)² subject to an Inertia-Augmented Phillips Curve stated as: nt+1 = t - c(U₁U₂) and an IS curve stated as: (Ut+1- Un) = f(rt-rs), derive the interest rate rule followed by the policy-maker.
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- Assume that α = β = 1, derive the MR curve graphically using the tangencies between the loss circles and the Phillips curves. With reference to the diagrams, explain the effect of the following (in each case, assume all other parameters are held constant):(a) An increase in the slope of the Phillips curve, α (b) An increase in central bank’s inflation aversion, β.Assume that α = β = 1, derive the MR curve graphically using the tangencies between the loss circles and the Phillips curves. With reference to the diagrams, explain the effect of the following (in each case, assume all other parameters are held constant):(a) An increase in the slope of the Phillips curve, α.An economy has the following equation for the Phillips Curve: π = Eπ − 0.5(u − 6)People form expectations of inflation by taking a weighted average of the previous two years of inflation: Okun’s law for this economy is: Eπ = 0.7π−1 + 0.3π−2 (Y −Y−1)/(Y-1)=3.0−2.0(u−u−1) Th economy begins at its natural rate of unemployment with a stable inflation rate of 5 percent. 1. What is the natural rate of unemployment for this economy? 2. Graph the short-run tradeoff between inflation and unemployment that this economy faces. Label the point where the economy begins as A. 3. 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, label the point the economy experiences that year as point B.
- For this question, assume that the Phillips curve equation is represented by the following equation: πt - πt-1 = (m + z) - αut. A reduction in the unemployment rate will cause A) a reduction in the markup over labor costs (i.e., a reduction in m). B) an increase in the markup over labor costs. C) an increase in the inflation rate over time. D) a decrease in the inflation rate over time. E) none of the aboveAssume that an economy is governed by the Phillips curve π= πe – 0.5(u – 0.06), where π= (P – P–1)/P–1, π e = (P e – P–1)/P–1, and 0.06 is the natural rate of unemployment. Further assume π e = π–1. Suppose that, in period zero, π= 0.03 and πe = 0.03—that is, that the economy is experiencing steady inflation at a 3-percent rate. a. Now assume that the government decides to impose whatever demand is necessary to cut unemployment to 0.04. Suppose the government follows this policy for periods 1 through 5. Create a table of π and πe for these five periods. b. Assume that, for periods 6 through 10, the government decides to hold unemployment at 0.06. Create another table of π and πe for these five periods. Is there any reason to expect the inflation rate to go back to 0.03? c. If the government persisted in its behavior under part a, do you think the public would continue for long forming expectations according to πe = π–1? Why?Suppose the Federal Reserve sets the real interest rate to 1.5%. Moreover, assume that there are no demand shocks, that b = 2.5, and that F = 0.02. If the resulting change in the inflation rate is +0.375 percentage points, what is the value of the parameter D? (Round to the nearest hundredth.) Hint: Use the IS and Phillips Curves to calculate your answer.
- The Philips curve in an economy is given by a = Επ- 0.5 (u - 6). Assume that the economy starts out at its natural unemployment rate and expected inflation Ex = 5.25%. If output decreases by 2%, using Okun's Law and the Phillips curve relation, what is actual inflation π ?Assuming a = ß = 1 in the Loss function and the Phillips curve, derive the MR curve graphically and explain the economic intuition behind the process.Šuppose that the Phillips eurve is nt the number of employed workers. Further assume that the size of labor force is 200. Rewrite the Phillips curve equation in terms of output gap. = Tet – 0.5(ut - un ), and the aggregate production tt tn function is Yt = Nt, where Nt is
- The Phillips Curve equation of the DAD-DAS model is nt = Et-1nt + p(Yt – Ýt) + vt. According to this equation, firms raise prices when output is ____________ the natural level of output, or equivalently, when the unemployment rate is _________ the natural rate of unemployment. a. above; above b. above; below c. below; below d. below; aboveA policy-maker minimises a loss function of the form: V = [u – (un – k)]² + a(n – n°)² subject to current given conditions for the economy stated as u = un – b(n – n°) + E. Price and wage setters are endowed with rational expectations. Derive the time consistent rate of inflation.Consider a version of the Phillips curve where a proportion of wages, 1 >> 0, are now indexed to the rate of inflation. In these labor contracts, nominal wages move one-for-one with the actual price level. The remaining proportion of wages, (1-2), are set on the basis of expected inflation: nt λnt (1) et+ (m+z)-aut (2) a. Suppose that лet=πt-1. Solve for the natural rate of unemployment (the rate such that t=t-1). Is the natural rate of unemployment different as a result of wage indexation? b. Re-write the Phillips curve in terms of the difference between чt and un using the value for un you calculated in (a). How does wage indexation impact the way changes in inflation respond to deviations of the unemployment rate from the natural rate? What is the intuition for this result?