QUESTION 3 [20 marks] 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) = $3 + w/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 mction 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 U051, b) = a2 + 62. 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 shepper 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 + 2?; = 2, 000. 4. [3 marks] If the mother's utility functiOn is 1701, 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 (a,b) = % %, which child will get more money? Why? Which child will consume more goods? Why