Microeconomics

Suppose you are a member of the successful newcomer band "The Public Good Providers". "The Public Good Providers" have three fans, Claus, Soren and Niels, who have already purchased tickets for a concert of your band. Assume that there are no other guests at the concert. If your band practices, this increases the quality Q of the concert. Claus, Soren and Niels consider paying your band for practicing, and your band has offered them to practice as many hours as they want in return for receiving one kroner per hour. Music quality will be 0 without practice and increase by one unit with each hour of practice. However, while Soren places great importance on the music being of high quality, Niels places not so much importance on it, and Claus does not care at all about the quality of the music and only goes to the concert to hang out with the others. They have the following utility functions, where ro, Is and Iy are the amounts of money Claus, Soren and Niels "consume" in the end, respectively: uc(Ic) = IC us(xs, Q) = 15 + 4vQ UN(IN, Q) = IN + 2VQ where up denotes Claus' utility function, us denotes Soren's utility function, and wy denotes Niels' utility function. Niels, Claus and Soren each have an endowment of 100 kroner. a) What levels of the public good of music quality Q", Q", ON will each of the three contribute if they make decisions individually and take the other players' decisions as given? What is the total amount provided? b) What is the socially optimal level of music quality? c) Your band understands that Claus, Niels and Soren will buy less music quality than the socially optimal level. Your band therefore decides to try to overcome this problem by letting them pay Lindahl prices. What are the Lindahl prices to, 15, to that each of the three fans would have to pay in the Lindahl equilibrium? d) Why may Claus, Niels and Soren be unwilling to truthfully provide the information you need to calculate the socially optimal level of the public good and the Lindahl prices? Explain in words. Your band decides to set up the Vickrey-Clarke-Groves mechanism to elicit the willingness to pay for music quality from Claus, Nicks and Soren. For simplicity, assume that music quality can be either 0 or 16. Your band decides to offer to provide music quality of 16 at a total price of 15, where each of the three would have to pay 5 kroner for the provision of the public good. e) What are Claus', Niels' and Soren's net utilities, no, ny and ng, for going from music quality of 0 to music quality of 16 if each of them has to pay 5 kroner for the provision of the public good? f) Assume that the Vickrey-Clarke-Groves mechanism is successful in the sense that all three report their true net utilities. Will the public good be purchased? Which agent is pivotal? What is the Clarke tax that this agent will have to pay