5. In class, we examined and solved the following model: There are two types of jobs in a society: a low-skilled job called job A and high-skilled job called B. People are free to choose either A or B but not both. There are high-ability people who can work in A or B. Low-ability people can only work in A. If a low-ability person works in a job A, her annual income (net of effort) is $100. If a high-ability person works in job A, her income (net of effort) is $200. If a high-ability person works in job B, her annual income (net of effort) is $400. There are 50 high-ability people and 100 low- ability people. Assume that if a high-ability person is indifferent between working in A or B, then she will choose to work in B. The government does not know the identity of high- ability agents or low-ability agents. However, the government wants to distribute income from high-ability people (i.e., the rich) to low-ability people (i.e., the poor). If a worker chooses job B, the government can correctly infer that she is a high-ability person. Let's tweak this model one more time (we are beating the model to death, huh?). This time assume that high-ability people care about low-ability people, so a dollar taken from a high-ability person and given to a low-ability person is considered as a loss of a dollars, NOT as a loss of one dollar, where 0 < a < 1. As discussed in class and in the solution to assignment 2, there are economists and other social scientists who have argued that people are willing to support redistributive policies if a higher proportion of the beneficiaries belong to a group that they can identity with. Conversely, people prefer less redistribution when members of their own group constitute a smaller proportion of the beneficiaries. This form of group loyalty may take the form of religion, race, ethnicity, etc. Therefore average support for redistribution declines as demographic heterogeneity increases. We argued that this might explain why there is less redistribution in a demographically heterogeneous country like the USA compared to a homogeneous country like Finland. Using the model above and taking cognizance of the following two conditions: (a) Pareto efficient allocation of workers to jobs is preserved, and (b) total tax revenue is shared equally among all workers in job A, prove the claim that the more people care about each other, the more redistribution can a government undertake, even if it has incomplete information.