Answer Happy

3. Suppose that there are 1,000 surfers in Auckland and the only places that Aucklanders can surf are Piha and Muriwai. Each surfer surfs once each day and his/her daily utility obtained from surfing is a simple function of where s/he surfs and the number of other surfers in close proximity. Specifically, daily utility obtained by each surfer at Piha is U=1000-Nº, where Nº is the number of surfers who visit Piha each day. Daily utility obtained by each surfer who surfs at Muriwai is UM = 600-NM/4, where NM is the number of surfers who surf at Muriwai. a. Write an expression for the number of surfers that surf at Piha as function of NM. [1 point] b. Suppose that each surfer is free to choose where to surf and maximizes his/her utility. i. How many surfers will surf at Piha? How many will surf at Muriwai? [4 points] ii. What will be the daily utility of a surfer who surfs at Piha? What will be the daily utility of a surfer who surfs at Muriwai? What will be the surfing community's aggregate daily utility (the sum of all surfers' daily utility)? [3 points] c. Suppose that you work for the Auckland City Council (ACC) and are asked to determine a policy to maximize the surfing community's daily utility. i. Write an expression for the aggregate daily utility obtained by the surfing community as a function of NM [3 points] ii. Determine the number of surfers that should surf at each beach that maximizes the surfing community's daily utility. [6 points] iii. If each surfer values utility at a constant rate of $0.01 per unit, what fee should the ACC charge individuals who surf at Piha so that surfers are indifferent between surfing at Piha and surfing at Muriwai? [3 points] iv. If the ACC divides the revenue from the fee equally among Auckland's 1,000 surfers, show that each surfer is better off than s/he was in the situation in (b) and evaluate the gain per surfer in dollars. [4 points] d. Using words that decision makers at the ACC (who do not have backgrounds in economics) will understand, explain why charging a fee to surf at Piha increases the aggregate welfare of the surfing community relative to not charging a fee. [6 points]