Question 3. Suppose there are two statesA and Bthat border one another. State A has 1 poor person living in it. State B has 10 poor people living in it. Any poor person can move states at any time for a cost of $100. The government of State A would like to give some money to the poor. Suppose that State A's government's payoff from giving an amount of money, 1:, to the poor is equal to 1000i t2. This implies that the government of State A would be willing to give up to $1000 to the poor and would most like to give $500. However, it also implies that the government of State A would prefer to give nothing to the poor than give more than $1000. The government of State B is uninterested in helping the poor. 1. The government of State A notices it has only 1 poor person and sets up a program whereby any poor person living in State A is entitled to $500. Has the government of State A implemented a policy that is consistent with its goal (as dened by its utility function) of supporting the poor while giving away no more than $500? If so, why? If not, what is the problem? 2. Suppose the government of State A is not allowed to discriminate among its poor 1 residents. It can only choose policies of the form \"we give X dollars to each poor person living in State A.\" Given its goals (as dened by its utility function), what is the best such policy that the government of State A can implement? 3. What happens to this policy if the number of poor people living in State B increases? Why