Consider the following citizen-candidate model. Citizens have a one-dirnensional policy pref- erence pi, which is distributed uniformly on [0. 1]. Each citizen gets higher utility the closer the implemented policy is to her preference. Each citizen votes1 but she can aLso choose to [1111 for ofce by paying a cost (5 > 0. After the election, the winning candidate implements her preferred policy. The utility function of citizen 3' is thus given by: U_ : _ I?! _ Pwinncrl _ a If i IILEIH t _ lpi _ Pwinncrl if 15 ("108511313 run where pwinnm. is the policy implemented by the winning candidate. If nobody rims for ofce, then a policy is selected uniformly at random from the interval [0. 1]. 1. Why do winning candidates always implement their own preferred policy? (a) Because it increases their chances of rte-election (b) Because it requires the least an101mt of effort (c) Because other candidates prefer it (d) Because it maximizes their own utility 2. We are going to try to characterize the equilibria of this game. Let's start by thinking about the equilibrium where nobody runs. Note that if only one citizen runs for ofce, she will win the election with certainty. (a) If nobody is running1 when will citizen 1' want to rim? i. First blank: A. U(r1ms) B. Ui (doesn't rim} C. 0 ii. Second blank (this is given): greater than or equal to iii. Third blank: A. U.- (nuns) B. Ut- (doesn't rim) C. 0 (h) The mathematical expression of this is (5' E % p.11 p,;). if citizen i has policy preference 1),; = 0.1, then what is the greatest cost he or she is willing to incur? Enter mnneric, with two places after the decimal. (c) If a candidate is willing to incur a cost of 11p to 0.5, then what is their policy position? Select all that apply