Problem Set 4 1. For the political agency model with rational expectations that we exam ined in class, show that the incumbent's probability of Winning relection in the second period is given by so that the density of the competence distribution is simply 5. You may refer back to the slides for Political Agency for details on the model if needed. 2. Use your result in question 1 to calculate the rstorder conditions for the incumbent politician's expected utility maximization problem aw; :r1+pI/3(R+r). 1 3. From the rstorder conditions and the rational expectations requirement that r1 : Flcomplete the equilibrium calculation in the slides and show that p; : g