Due to the ambuguity associated with the answer key for question 3 from the first homework assignment, I wanted to first highlight that for part B of this question, the curvature of the Charlie's indifference curve does in fact "flip" when the labels of the axes are switched. However, when coming to this conclusion, I found myself asking a much more interesting question; "In which direction would the indifference curve be bowed, when garbage is on the x-axis and smoothies is on y-axis?" And that's the extra credit question I pose to you, however, I will elaborate. What I want to know, is under what assumptions about garbage (the bad) and smoothies (the good) will the indifference curve be bowed towards the bad and bowed towards the good? Hint: This question is asking what assumptions about total utility (TU) and marginal utility (MU) of "goods" and "bads" must be true for the indifference curve to bowed in a particular direction (towards the good or bad) given that the slope of the indiffernce curve is equal to the MRS. It is usually assumed that goods have diminishing returns, meaning the TU will increase at a decreasing rate and MU will be positive and downward-sloping. However, what about bads? What is the most realistic relationship between bads and TU and bads and MU? Given this relationship (the assumption), will the MRS on an indifference curve increase or decrease (determined by the direction the indifference curve is bowed)?

To answer this question please provide any mathematical, graphical, or written explanation as is needed.

Attachment:- problem_set_1.zip