(a) Suppose Mark and Nancy each set a price of $4 per ice cream cone. How many customers will each get? (Hint: Let a be the location of the consumer who is indifferent between getting a cone from Mark and getting a cone from Nancy. Write down a consumer surplus equation and then solve for 93 in terms of the Mark and Nancy prices.) (b) Nancy cuts her price to $3.75. How many customers will she get now? Use your ndings to compute Nancy's demand elasticity at a price of $4. (c) If the marginal cost of an ice cream cone is $2, then is $4 the profit-maximizing price for Nancy, assuming Mark's price is $4? Extend your discussion here to address the following: What is the Nash Equilibrium of the game in which Mark and Nancy choose prices to maximize their prots? (d) Pioneer Day is an ofcial Utah holiday celebrated on July 24. The summer crowds double to 8,000! Assuming travel costs (represented by 1') do not change, how does this change Nancy's demand elasticity? Will Mark and Nancy want to raise or lower their prices for the holiday? (e) The Honorable Mr. Logan Provo is a Utah State Senator who represents Box Elder County, which is home to Brine Shrimp Beach. Senator Provo is constantly on the lookout for public works projects in his district. He proposes state funding for a Brine Shrimp Beach Boardwalk. This boardwalk, which will run the length of the beach, would mean that ice-cream customers no longer have to walk miles on loose sand to purchase a wafe cone. Vacationers would therefore be more willing to walk, and the value of t which repre 1 sents how much vacationers dislike walking 7 will fall to 4 What would Nancy's demand elasticity at $4 be, assuming Mark keeps his price at $4? (f) Senator Provo visits Nancy in her sprawling corporate campus in Park Valley. He explains that the BSB Boardwalk would make it easier for customers to reach Nancy's ice cream truck, and asks her to support his re-election campaign. Nancy explains that she thinks the Boardwalk is a terrible idea, and that she plans to give a large campaign contribution to Senator Provo's opponent Ms. Sandy Duchosne in the next election. Why is Nancy opposed to this project? (Hint: What is the Nash Equilibrium of the game in which Mark and Nancy choose prices to maximize their profits 7 if t is lower?)