Consider a small town being built for potentially interested residents, who differ in terms of their preferences over the size of the public park (small "s", or big "b") and the quality of the public school (average "a", or great "g") in their neighborhoods. The mayor of the town would like to form a number of neighborhoods, where the only differences among the neighborhoods are going to be the size of the public park and the quality of the public school they will offer.

a. If funding is no problem for the mayor, and preferences for school quality and park size are independently distributed across residents (i.e. no correlation between residents' preferences for park size and school quality), how many neighborhoods would need to be formed to make everyone satisfied?

b. How would your answer to part a change if anyone who prefers a big park to a small park also prefers average school quality over great school quality?

c. How would your answer to part a change if residents also differ in terms of their income levels ("l" or "h"), and their preferences for park sizes and school quality levels are perfectly correlated with their income level ("h" prefers "b" over "s", and "g" over "a"; and vice versa for "l")?