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Consider a central bank that is dominated by the political party that is in power (so there is no central bank independence). This question will work through the effect of elections on macroeconomic out- comes. The notation is: Ut is unemployment in period t, it is inflation period t, and the two are linked according to a Phillips curve: Ut = UT - (mt - TT f ) Agents' expectations of inflation of are formed rationally and are set before the central bank chooses inflation. [21 marks] Assume that there is a single party in control of the central bank, whose utility function is given by: Ut = -0tut - 0.5(mt)2 for a parameter # > 0. Solve for the inflation chosen by the central bank? Solve also for expected inflation, and for unemployment in equilibrium in this economy. Is there an inflation in this economy, and why? [4 marks] (b) Imagine instead that there may be a different party in power, whose preferences are different, since it maximizes instead: -Otut - 0.5(nt - #)2 where 7 > 0 is a parameter reflecting its higher tolerance for inflation. First, solve for inflation, chosen by this new party. Then, assume that when the private agents form expectations they do not know which party will be in power, but put a probability of 1/2 that each of the parties will be in power. Solve for expected inflation and unemployment when this new party is in power. Is unemployment always at the natural rate in this economy and why (or why not)? As parties alternate in power, do inflation and unemployment rise/fall/stay the same and why? [4 marks] (c) Now assume that agents know which party will be in power. Also assume that the natural rate of unemployment is zero, up = 0. Show that utility is Ut = -0.50? no matter which party is in power. What is the intuition for why utility is lower when O is higher? [2 marks] (d) The economy goes on for three periods and preferences over time are given by: U1 + U2 + U3 Moreover, there is a technology that allows society to have # be different over time subject to the constraint that 01 + 02 + 03 = 3 so that on average the parameter is 1 across all the periods. Solve for the optimal choices of 01. 02, 03- Explain intuitively how they are related. [3 marks](e) Consider again elections. The party in power at period 1 now realises there is a 0.5 probability it will be out of power forever from next period onwards. Therefore, her preferences at period 1 are U1 + 0.5(U2 + U3) Solve now for its choice of 61. Is it higher or lower than in the previous question. Why? [4 marks] (f) Say that period 2 arrives, and the party is still in power. It realises again that there is only a 0.5 probability that it will be in power in the final period, so that its preferences in period 2 are: U2 + 0.503 What is the optimality condition linking 62 and @3? Do you expect A to fall/increase/stay the same over the three periods and why? How does this differ from the solution to question d) and why? [3 marks] (g) The first part of this question, with the two parties that alternate in power, and the second part, with the party that fears not being in power in the future, are two examples of elections causing inconsistencies in intertemporal decision making. What are the names of these two inconsis tencies? [1 mark]
