Researchers noted that the relationship between Nearby Park Space (PS) and the willingness to pay by residential buyers in a city can be represented by B= 150,000+ 10000* PS for a "standardized lot" of 1/30th of a hectare and controlling for other aspects of the quality of a house. PS is measured in hectares. The question for a developer who is designing a subdivision is: how big should the park be? Assume that the subdivision is designed so that all homes in the subdivision can enjoy all of the park space equally, that the developer has no other properties nearby and that the developer sells at a price equal to what buyers are willing to pay. a) If the developer has 20 hectares of land to build on, what is the revenue maximizing value of PS? b) Without using numbers, explain why would a developer (who is also trying to maximize total revenue) with a smaller plot of land (say 5 hectares) build less park space as a proportion of their plot? c) Suppose that the developer has yet to buy the 20 hectares. (For this calculation, ignore the costs of building homes on the land.) i) Would they be willing to pay $3,000,000 per hectare for this land? ii) Would they be willing to pay $5,000,000 per hectare for this land? iii) What is their maximum willingness to pay (per hectare) for this land? For part iii) of this calculation, ignore the costs of building homes on the land.