Pillars of prosperity [10 marks] 6. Besley & Persson (2011) show that existing wisdom surrounding elements of institutions - e.g. state weakness, state fragility, inclusiveness, cohesiveness, etc. - can be summarised in a model where three pillars co-evolve to support economic prosperity. Refer to the model, as discussed in class, to answer the following questions. (i) Name and briefly describe the three pillars. [1 mark] (ii) Write down the incumbent's utility, and derive the level of public goods g,. Carefully describe your steps to obtain the mathematical expression for g, - [4 marks] (iii) Show mathematically that g, is inefficient from a social planner's perspective. Explain. [3 marks] (iv) The model, as discussed in class, assumes that the two groups are of equal size. How would your conclusions to parts (ii) and (ii) change if there was one large (majority) group and a small (minority) group? [2 marks]