i) Assume that PS (Park Space) is measured in hectares
ii) Assume that a= 0.7
iii) Ignore costs related to constructing a building. (I.e. this question is all about the developer's revenue not its profit.)
Researchers noted that the relationship between Nearby Park Space (PS) and the willingness to pay by residential buyers in all parts of the province can be represented by
B= 10+ a* PS
for a "standardized lot" of 1/20 of a ha. and controlling for other aspects of the quality of a house.
a) If you were a developer with 10 hectares of land to build on and the lot for each house occupied 1/20 of a hectare, what is the revenue maximizing value of PS? (At the development stage, the cost of land is a fixed cost.) 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 property nearby and that the developer sells at a price equal to what buyers are willing to pay. Finally, assume that 1 hectare is 100,000 square feet (which is roughly accurate).