3. Consider a Paper Factory {PF}, which usEs input 5? to produce its product. pollutes the environment that harms an Apple Producer (AP). Sinoe the PF has the legal right to pollute, the AP has to bribe the PF it' it wants PF to reduce pollution. The benefit function of PF {before input costs] is H = 20}. - y}. the price of input 3* PF = 2. and the damage function of AP is D = vi. (a) How much will PF pollute in the absence of an}r bargaining {assuming that it has the property right}? What is the efficient solution? ['5' pts} {b} Draw a diagram and show market equilibrium outcome and efficient solution. Calculate the Pigouvian tax required to achieve the efficient solution and show how this tax achieves the efficient solution in your diagram. {6 pts} (c) Nest. consider a bargaining solution. Calculate the amount AP has to bribe to PF so that I'F will reduce its pollution to the efficient level [assu ming a competitive bargaining]. What is the minimum compensation PF requires to reduce pollution from the market to efficient level? {'2' pts}