II. Long Problems Long Problem 1 (30 pts.) (Explain your answers!) Tom has preferences over fitness classes (good 1) and action movies (good 2), which he consumes in quantities 21 and 32, respectively. His preferences are described by the utility function U(1, 12) = 17- 12. Tom's income is m = 120, and unit prices are p1 = 4 and p2 = 2. a) (i) Find Tom's demand function for fitness classes, good 1. Explain your procedure, and describe the main characteristics of the demand function in words. (ii) Which consumption bundle (x;, r;) will Tom choose for the given market prices? Compute and graph his optimal choice (label everything), and explain briefly. b) The government wants to raise R = 8 dollars in tax revenues from Tom through an ad valorem sales tar on good 1. Which tax percentage " achieves this goal? Explain your computations, please. c) [ignore b)] Tom finds out that on some days, his beloved action movies cost only pz = 1. Also, a fitness studio offers tryouts where the first 10 fitness classes are free. (i) Graph Tom's new budget constraint in this situation (label everything, and give slopes). (ii) Find the mathematical formula for his budget constraint (be precise). (ii) Compute and graph (you can use the graph in (i)) his new optimal consumption choice. d) (ignore b) and c)] Tom spots the following ad. (i) His favorite fitness clubs PIPES offers basic memberships (which include 40 visits/month) for just 84 dollars. Should Tom become a member, or not? (ii) Tom realizes that as an econ student, he doesn't have time to consume more than a combined total of 42 fitness classes and/ or action movies per month (assume the time requirement for movies and fitness classes is the same). How many fitness classes and action movies will he consume, if he chooses to become a member? Should he still accept the membership offer? Explain your steps precisely