please can you provide explanation of the utility finctions

2. Consider the following utility functions: (a) U(x, y) = ry. (b) U(x, y) =12y?. (c) U(x, y) = Inx + Iny. Show that each of these has a diminishing MRS but that they exhibit constant, increasing, and decreasing marginal utility, respectively. What do you conclude? 3. (a) A consumer is willing to trade 3 units of x for 1 unit of y when she has 6 units of x and 5 units of y. She is also willing to trade in 6 units of x for 2 units of y when she has 12 units of x and 3 units of y. She is indifferent between bundle (6, 5) and bundle (12, 3). What is the utility function for goods x and y? Hint: What is the shape of the indifference curve? (b) A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle (8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consuming bundle (4, 4). She is indifferent between these two bundles. Assuming that the utility function is Cobb-Douglas of the form U(x, y) = xy, where a and B are positive constants, what is the utility function for this consumer? (c) Was there a redundancy of information in part (b)? If yes, how much is the minimum amount of information required in that question to derive the utility function