1. Jenn has a fixed amount of time 20 hours (per week) that she allocates toward studying for her economics classes and her marketing classes. Let to be the amount of time (in hours) devoted toward economics and to be the amount of time devoted toward marketing. Assume initially that a unit of time devoted to the study of marketing constrain the student equally. Thus, the student's budget constraint is simply te + tM = 20. Assume that Jenn's preferences over study times (tz, tM) is described by a utility function with all of the standard properties (monotonicity, convexity, both goods essential) and that Jenn's preferences are identical in all parts of the problem. (a) At lunch with the economics professor, the marketing professor made the following statement "If Jenn had more than 20 hours to study each week, then she would spend more time studying marketing." Given what we learned about the resource splitting problem, can we conclude that the marketing professor's statement is always correct? Relate your answer to course concepts or explain it with a figure. (b) Item how does your answer relate to the concept of a "normal good"? (c) The economics professor responded with the following observation "If you make the marketing class tougher, then Jenn will devote more time to studying for it, even if her total study time stays the same." Suppose that if the marketing professor makes the class tougher, then it is more costly for Jenn to spend time studying for it. In particular, if the marketing class becomes tougher, then each hour that Jenn devotes to studying marketing feels like 2. In other words, if the marketing professor follows this advice, then Jenn's budget constraint will be te+2tM = 20. Is it possible that the economics professor is correct? Is the economics professor always correct? Relate your answer to course concepts or explain it with a figure. (d) How does your previous answer relate to the concept of a "Giffen good"? (e) Suppose the marketing professor is correct in part (a). Furthermore, suppose that this is true for any time budget. In other words, if Jenn's total available study time increases, she increases the amount of time she devotes to marketing. Is it possible that the economics professor is also correct in (b)? (Hint: Can a Giffen good be normal?)