4. The formation of expected inflation The text proposes the following model of expected p t e = 1 1 - u 2 pQ + u p t - 1 7. and expected inflation is given by inflation a. Describe the process of the formation of expected inflation whenu=0. b. Describe the process of the formation of expected inflation whenu=1. c. How do you form your own expectation of inflation? More like a, or more like b?
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Step 1: Understand the given model of expected inflation: \[ p_t^e = \frac{1}{1 - u^2} pQ + u p_{t-1} \] where \( p_t^e \) is the expected inflation at time t, \( pQ \) is a constant, and \( u \) is a parameter. Show more…
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The text proposes the following model of expected inflation πₜᵉ = (1 − θ)π̄ + θπₜ₋₁ a) Describe the process of the formation of expected inflation where θ = 0 b) Describe the process of the formation of expected inflation where θ = 1 c) Suppose that the Phillips curve is given by πₜ = πₜᵉ + 0.1 − 2uₜ. What is the natural rate of unemployment for this economy? d) In addition, suppose that πₜᵉ = πₜ₋₁. Assume inflation in t-1 is zero. Suppose also that in year t, the central bank decides to keep the unemployment rate at 4% forever. Compute the rate of inflation for years t, t+1, and t+2
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Consider a discrete-time version of the analysis of money growth, inflation, and real balances in Section 12.1. Suppose that money demand is given by mt − pt = c − b(Et pt+1 − pt), where m and p are the logs of the money stock and the price level, and where we are implicitly assuming that output and the real interest rate are constant (see [12.77]). (a) Solve for pt in terms of mt and Et pt+1. (b) Use the law of iterated projections to express Et pt+1 in terms of Etmt+1 and Et pt+2. (c) Iterate this process forward to express pt in terms of mt, Etmt+1, Etmt+2, .... (Assume that lim i →∞ Et[{b/(1 + b)}i pt+i ] = 0. This is a no-bubbles condition analogous to the one in Problem 8.8.) (d) Explain intuitively why an increase in Etmt+i for any i > 0 raises pt. (e) Suppose expected money growth is constant, so Etmt+i = m t + gi. Solve for pt in terms of mt and g. How does an increase in g affect pt ?
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