Please answer all parts!

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 U01, 5) = V'E + VIE, 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{o,b) = min {LLB}. How will she choose to divide the money? Why? Suppose that her utility function is Ups, b} = max {o,b}. How will she choose to divide the money? Why? 3. [4 marks] Suppose that her utility function is U(a,b) = a2 + 52. 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 he the amount of musumptiou goods that A gets and bthe amount that B gets. We will measure consumption goods so that one unit of musumptiou goods costs $1 for A and $2 for 3. Thus the parent's budget constraint is a + 20 = 10$). 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 U031 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