1. Consider the Benabou model. (a) There are two districts in the city. Suppose that district C* has 30% and district 70% of the city's housing stock. Also, 30% of households in the city are type A high income (human capital) households and 70% are type B low income (human capital). Let ha and hs denote the respective human capital of the parents of types A and B households, p! and p? the respective rents in districts 1 and 2, x* and x? the respective fractions of type A households in districts 1 and 2 and V the indirect utility function. (i) (5 points) Suppose that C! is the high-income district in a segregated equilibrium; i.e., x! > x2. Can the equilibrium rents be such that that V(hg, p, x!) > V(hs, p?, x*)? Why or why not? (i) (5 points) Suppose that C? is the high-income district in a segregated equilibrium; i.e., x* > x*. Can the equilibrium rents be such that that V(ha, p*, x*) > V(ha, p? x*)? Why or why not? (b) (12 points) The UK shows low levels of social mobility, meaning that there is a high correlation between parent and children's income or other socio-economic indicators. What are the conditions in the Benabou model that may cause the high correlation? Explain. What policy interventions may counteract the effects of each of those conditions that cause the high correlation