ser University Oct. 21" V#B 2. (Total: 14 points) Suppose your instructor (Josh) has decided he needs a new wardrobe and now that he has some money he wants entirely bespoke outfits (i.e. outfits designed and tailored for him). Suppose Josh's income is Y = $50,000 and Josh's utility over the clothing is given as: U(q, n) = 10 x q+30 x n where q is the quality of each outfit and n is the total number of outfits. As there is an issue finding someone to produce the quantity of clothing at the quality desired, let P = $200 be the price of either 1 outfit or an increase of quality by 1 with cost increasing as the square sum. Furthermore, Josh is fortunate to have a wife that agrees to provide him with food and shelter despite spending all of his money on clothes. In other words, Josh believes his budget constraint is $50, 000 = $200 x (q2 + n2) (a) (4 points) How many outfits will Josh purchase? What is the quality of the outfits? (b) (3 points) Suppose we have a budget constraint of $50, 000 = $200 x (q x n). Given Josh's utility function, would Josh be able to maximize his utility? Explain.(c) (7 points) In Figure 1 provide a sketch of the optimal choice, indifference curve, and budget constraint based on part (a). Show a sketch of the budget constraint from part (b) as a dashed line. Be sure to label all axes, lines, and important points. Would Josh ever throw all his money away on quality without every actually purchasing any quantity of the clothing? Explain why to why not with reference to your graph