1) Jane enjoys going to Karaoke (K) with her friends. A full night of Karaoke costs $30, and Jane's entertainment budget is $150. Using the concept of composite goods, Jane's utility is: U = ln (KY) 1 K' MUY MUK = 1 Y a) What is Jane's budget constraint? b) What is the formula for Jane's budget line? c) Maximize Jane's utility. d) Jane can join a Karaoke Club for $18, which would reduce the cost of Karaoke to $24. What are Jane's new budget constraint and budget line if she joins the club? e) Maximize Jane's utility if she joins the club. f) Should Jane join the club? Explain your answer. g) Show the result of (c) and (e) above on one graph. (Hint: use a large graph to make showing the changes clearer. Graph does not need to be to scale.) h) Graphically show a general example of how another consumer may make the opposite decision (join vs. not join) as Jane.