Suppose that three people are interested in purchasing one bagel each, and three people are interested in selling one bagel each. Ann is willing to pay $10 for one bagel, Bonnie $7, and Cam $4. Andy is willing to accept $8, Bobby $5, and Charlie $2. You can think of this scenario as a standard supply and demand setup. You can also view it as six people with six different valuations of having a single bagel (their \"reservation value\"). The buyers happen to not have a bagel, while the sellers happen to have a bagel in hand. (a) Under the standard supply and demand scenario, make a graph (two step functions) and gure out which three people end up with bagels given a market equilibrium. (b) The social surplus can also be viewed as the difference in surplus between the nal outcome relative to the initial allocation. The initial value is 8 + 5 + 2 : 15 since this is the value the three potential sellers place on having one bagel each. What is the total value to all six people given the market outcome? Based on this, what is the social surplus? (c) Conrm that you can nd this same social surplus as an area on your graph. Label the area S. (d) Suppose a nonmarket outcome is achieved (perhaps due to market intervention such as a price control or quota) in which Ann pays $9 to Andy for a bagel, while Bobby and Charlie each keep their bagel. (uAm(bagel,9) = vAnn(bagel) 9 = 10 9 = 1, uAndyMO bagel, 9) = 0 (9) = 9, \"Bonnie = 0; \"Bobby = 57 \"Cam = 0, uCham-e = 2). Demonstrate that this allocation is not Pareto efcient. [The main point of this exercise: When social surplus is not maximized, you can always nd a Pareto improvement .]