= = ) A park serves a population of varying tastes. There are N people, numbered from 1 to N. If the ith person uses the park, he gets utility diu(n), where n is the number of people using the park and u(n) 0.9. Anyone who does not use the park has utility v = 0.1. These N people are sorted by di which is di = 1 0.01 ~ (i 1). N = 100 and Q1 = 1, Q2 = 0.99,...,Q100 = 0.01. i. How many number of people are allowed to use, if the authorities try to maximize the sum of utilities of all the population (this is called as the utilitarian optimum)? ii. The authorities privatize the park. How many number of people use this park, if the private company sets the entrance fee so as to maximize profit? iii. How should the authorities tax the company in order to bring about the above utilitarian optimum? = = ) A park serves a population of varying tastes. There are N people, numbered from 1 to N. If the ith person uses the park, he gets utility diu(n), where n is the number of people using the park and u(n) 0.9. Anyone who does not use the park has utility v = 0.1. These N people are sorted by di which is di = 1 0.01 ~ (i 1). N = 100 and Q1 = 1, Q2 = 0.99,...,Q100 = 0.01. i. How many number of people are allowed to use, if the authorities try to maximize the sum of utilities of all the population (this is called as the utilitarian optimum)? ii. The authorities privatize the park. How many number of people use this park, if the private company sets the entrance fee so as to maximize profit? iii. How should the authorities tax the company in order to bring about the above utilitarian optimum