Question 5. Inflation and Unemployment (Discrete Time): Let pt , t , wt , m and T be actual inflation rate, expected inflation rate, growth rate in nominal wages, growth rate in money supply and growth rate in labor productivity respectively. Let the economy be characterized by following system of equations: wt = Ut + t with , > 0; 0 < 1 : Evolution of Wages; pt = wt T : Evolution of Actual Inflation; t+1 t = (pt t) with 0 < 1 : Adaptive Expectation & Ut+1 Ut = (m pt+1) with > 0 : Evolution of Unemployment where Ut is the unemployment rate at time t.

(a.) Combine above equations and derive a second-order difference equation in terms of pt .

(b.) Derive the steady state value of pt .

(c.) Discuss the stability property of steady-state for each type of characteristic roots.

(d.) Derive the expression for the steady-state value of unemployment rate.