A parent has two children named A and B and she loves both of them equally. She has a total of $2,000 to give to them.3 1. [3 marks] The parent's utility function is U(a, b) = x/E + , where a is the amount of money she gives to A and b is the amount of money she gives to B. How will she choose to divide the money? Why? 2. [3 marks] Suppose that her utility function is U(a, b) : min {(1, b}. How will she choose to divide the money? Why? Suppose that her utility function is U (a, b) : max {a, b}. How will she choose to divide the money? Why? 3. [4 marks] Suppose that her utility function is U(a, b) : a2 + b2. How will she choose to divide the money between her children? Explain why she doesn't set her marginal rate of substitution equal to 1 in this case. Now, suppose that A is a much more efcient shopper than B so that A is able to get twice as much consumption goods as B can for every dollar that he Spends. Let a be the amount of consumption goods that A gets and b the amount that B gets. We will measure consumption goods so that one unit of consumption goods costs $1 for A and $2 for B. Thus the parent's budget constraint is a + 2b : 2,000. 4. [3 marks] If the mother's utility function is U(a, b) : a + b, which child will get more money? Why? Which child will consume more goods? Why? 5. [3 marks] If the mother's utility function is U(a, b) : a. x b, which child will get more money? Why? Which child will consume more goods? Why? 6. [4 marks] If the mother's utility function is U (ct, b) : % %, which child will get more money? Why? Which child will consume more goods? Why