Y5

Answer the following questions as precisely and concisely as possible (I am looking for a maximum of 5-10 lines per question. Each part is worth 3 marks) (i) In the New Keynesian model, explain why price dispersion is costly for consumers and producers. (ii) What is the Taylor principle and why is it important? (iii) Why is price-level targeting superior than inflation targeting in the purely forward- looking New Keynesian model?

2. Suppose the economy is characterized by the following New Keynesian model: xt = Etxt+1 1 [it Ett+1] + ut (1) t = Ett+1 + xt + t (2) where xt denotes the output-gap, it the nominal short-term interest rate, t inflation rate, ut, a demand shock, t a cost-push shock and 0 < 1, > 0, > 0. Assume that the shocks follow the following proceses: ut = uut1 + ut (3) t = epst1 + epst (4) where the 's are white noise processes. The central bank sets the nominal interest rate, it to minimize: 1/2Et i=0 i [^2t+i + x^2t+i]. (5) where is the weight the central bank assigns to the stabilization of the output-gap at the expense of the stabilization of inflation. (i) Derive and interpret the first-order conditions for the optimal policy under discretion. [5 marks] (ii) Assuming that t = t, find [6 marks] (iii) Show that the central bank cannot perfectly stabilize inflation and the output-gap if there is a cost-push shock epst [2 marks] (iv) Prove that the Taylor principle is satisfied in the model. [3 marks]