Question 2. Dening Property Rights In a remote valley, two businesses share a waterway. Olivia's Rice Patties pumps water from a river and uses it to irrigate its elds. The used water eventually ows back into the river, carrying some of the fertilizer that Olivia applies to her crops. Up to a certain point, more fertilizer helps increase Olivia's harvest. Downstream, Randall's Riverfront Resort offers accommodations and ne dining to interested vacationers. Fertilizer contamination of the river creates algae blooms that adversely affect Randall's business. The functions describing the prots of each establishment are: now) = 108 + 32F .251?2 HR(F} = 560 * 24F where the subscripts \"O\" and \"R\" refer to Olivia's and Randall's places of business, respectively. \"F\" represents the amount of fertilizer int he river generated by Olivia. Recall that a prot function is H = TotaiRcoenue TotalCost 1] What is the marginal benet of fertilizer to Olivia? 2] What is the marginal cost of fertilizer to Randall? 3) Plot Olivia's marginal benet curve and Randall's marginal cost curve. 4] What is the optimal level of fertilizer according to Olivia? 5) What is the optimal level of fertilizer according to Randall? Suppose that the existing law denes property rights that favor recreational users of waterways such as resorts at the expense of farmers. A resort can sue a polluting farmer for prohibitive damages if any pollution takes place, unless the affected parties consent to an alternative agreement. 1) What is the amount of pollution that takes place in this scenario? 2) What are Olivia's and Randall's prots in this scenario? (Assuming that Randall has all the bar- gaining power such that he captures the entire Coasian bargaining surplus.) 3) Suppose the law had given the property rights to Olivia instead. What is the amount of pollution that takes place in this new scenario