Please submit via Gradescope. Question Missing Market (20pt). Adam and Bob are college roommates. Both Adam and Bob like to play violin (good x) and eat cake (good y). Adam and Bob each receives a monthly stipend, 14 and 1B respectively. Adam's utility function is given by: uf (x, y) = xyl-a Bob's utility function is given by: uB (x,y) = xbyl-b a. Calculate Adam's demands for both goods. (4pt) Adam is not very good at playing violin, and Bob dislikes hearing Adam's violin practice. Suppose Bob still has Cobb-Douglas utility function, in which Adam's violin noise has a power of c. Furthermore, Adam is entitled to practice violin at the dorm, and Bob has an option to pay Adam to reduce Adam's practice. b. Please set up optimization problems for Adam and Bob respectively. Denote the price of noise reduction as pz, the original demand of violin practice as Xo, and the reduced practice as z.(6pt) Let a = 0.25, b = 0.4, c = 0.2, IA = 200, and /B= 300. Set price of playing violin to 1. c. Calculate Adam's demand for playing violin as function of price of noise-reduction. (3pt) d. Calculate Bob's demands for playing violin as function of price of noise-reduction. (3pt) e. What is the price of noise-reduction? (4pt)