Brine Shrimp Beach is a perfectly linear beach running exactly cast/west on Utah's Great Salt Lake. The length of the beach is exactly four miles. Brine Shrimp Beach attracts throngs of vacationers each summer; on a typical summer day, 4000 people spread out evenly on its sandy, but also very salty, slope. Summer vacationers love gigantic 3-scoop waffle cones, so there are two ice cream stands (one owned by Nancy and one by Mark) that are located on Brine Shrimp Beach. Summer vacationers also hate walking. Each vacationer has a willingness to pay for one cone per day of $12- + + distance where "distance" is the distance from that vacationer's beach umbrella and towel to an ice cream stand. (Suppose vacationers never buy multiple cones in a day.) Nancy's stand is one mile from the west edge of the beach, while Mark's is three miles from the west edge (and hence one mile from the east edge). Suppose, for now, that t- (a) Suppose Mark sets a price of pm and Nancy sets a price of Pn. How many customers will cach get? (Hint: Let z be the location of the consumer who is indifferent between getting a cone from Mark and getting a cone from Nancy. Note that z will be a number between zero and four representing how far this customer is from the west edge of the beach and further that z will depend on the two prices. Write down a consumer surplus equation and then solve for r in terms of the Mark and Nancy prices. Be sure to derive and explain this equation as part of your answer.) (b) Suppose the price of a cone at both stands is $4. How many customers will Nancy get? (c) Nancy cuts her price to $3.75. How many customers will each get now? (d) Use your findings from (b) and (c) to compute Nancy's demand elasticity when her price is $4 and Mark's s $4 as well. (e) Repeat your analysis from (a) through (d) above assuming t. Explain both how and why Nancy's demand elasticity changes when t changes.