Five homeowners live on the shore of Lake Ontario: Ava, Ben, Clare, Dave, and Ethan. In the summer, there are lots of mosquitoes. Let x denotes the number of tankfuls of mosquito spray that are sprayed each week during the summer. Concerning the mosquitoes, the five residents marginal willingness to pay schedules for x are given by: Avas marginal WTP = 30 x; Bens marginal WTP = 27 x; Clares marginal WTP = 24 x; Daves marginal WTP = 21 x; and Ethans marginal WTP = 18 x. There are several local companies that will spray to control mosquitoes. The firms all charge the same price, p = $40 per tankful they spray. Therefore MC = $40. Answer all the following questions:

1). Is there a Pareto efficient amount of bug spray for the five residents? If so, please compute the optimal amount of spray. Draw the graph. 2). If the five homeowners each contact with the bug-spray companies separately, how many tankfuls of the spray each of them will purchase? Is there any free rider problem? Explain. 3). The homeowners decide to form a homeowner association (HOA) to deal with the mosquitos. The HOA will charge each of them only a share of the $40 price. Please find the Lindahl prices. Given the Lindahl prices, the HOA will ask each homeowner how many tankfuls of spray in total the HOA should purchase. Would they all agree on the same amount? If so, whats the amount of tankfuls of spray the HOA will purchase? Is it Pareto efficient? 4). Explain how the free rider problem is solved by Lindahl pricing. What are the advantages and disadvantages of the Lindahl pricing?