please can you explain those utility function

1. True or False? Explain. {a} True of False: The utility function given by u(:r1,:rg) = {;r1 3)2 represents preferences consistent with the six assumptions about preferences as discussed in class. {b} True or False: The utility function given by u(:rl, 1:2} = If +32 rep- resents preferences consistent with the six assumptions about prefer- ences as discussed in class. [c] Suppose Kwame had chosen his optimal bundle based on his budget set. After some price and income changes, Kwame realizes that he can no longer aord his old optimal bundle. True or False: Then he must be worse off than before. (explain your answer). 2. Suppose Slava's utility function is U (3:1, :2) = (3:1)\"1 (2:2) and his budget constraint is 15111 + par: = I. {a} Find the formula for an indifference curve that yields some utility c. Graph it. (b) Calculate the MRS at any bundle (31,122} {using marginal utilities}. [c] Now1 calculate MRS at any bundle (okra) by directly evaluating the slope of an indifference curve and show that your answer is the same as in part (b). (Hint: Set up an arbitrary indifference curve: a (11,322) = c. Differentiate both sides by :2. Then think about what \"c" means and substitute appropriately). {(1) Briey interpret how the MRS changes along an indifference curve- [e] Suppose Slava nds himself consuming a bundle where the indiffer- ence curve is steeper than the budget line. Explain why this is not his optimal bundle. 1. True or False? Explain. (a) True of False: The utility function given by n(:1:1,s:2) = (:r1 3)2 represents preferences consistent with the six assumptions about preferences as discussed in class. (b) True or False: The utility function given by 1411,32) = If +32 rep- resents preferences consistent with the six assumptions about prefer- ences as discussed in class. (c) Suppose Kwame had chosen his optimal bundle based on his budget set. After same price and income changes, Kwame realizes that he can no longer afford his old optimal bundle. True or False: Then he must be worse off than before. {explain your answer). 2. Suppose Slava's utility function is U (1'1, :2) = (1:1).I (m2) and his budget constraint is p131 +17ng = I. (a) Find the formula for an indifference curve that yields some utility c. Graph it. (b) Calculate the MRS at any bundle (171.32) (using marginal utilities). (c) Now, calculate MRS at any bundle ($1,332) by directly evaluating the slope of an indi'erence curve and show that your answer is the same as in part (b). (Hint: Set up an arbitrary indifference curve: \"($1,172) = c. Dierentiate both sides by 11:2. Then think about what "c" means and substitute appropriately). ((1) Briey interpret how the MRS changes along an indifference curve. (e) Suppose Slave nds himself consuming a bundle where the indiffer- ence curve is steeper than the budget line. Explain why this is not his optimal bundle