f. What kind of social coordination problem do you think exists between Mckenna and Natasha? Why? g. Now consider that there is a third -party that regulates how Natasha and Mckenna interact. Each of them must pay a tax in fish for each hour they spend fishing (fractions work because fish can be chopped up). That is, Mckenna would pay a tax per hour she fishes and Natasha would do the same. i. Construct each player's utility function including the tax (1). Given a tax (t) and the other player's effort, find each player's best response function ii. What is each player's Nash equilibrium level of fishing with the tax? What is each player's utility at the Nash equilibrium with the tax ? iii. How big should the tax be in units of fish per hour to make each player choose a Pareto-efficient level of time spent fishing? How many fish would each player catch and what would each player's utility be at the Pareto efficient outcome given that the tax authority gives back the fish it collects as a lump sum to each fisherman (the tax authority divides the fish equally among the fishermen independent of how much they fish)? h. Assume that Mckenna has price -setting power over Natasha (Mckenna is the 'leader ' in the interaction ). What is the (Stackelberg ) equilbrium amount of effort that each of the fishermen would exert ? How much fish would each get and how much utility would they each have at the Stackelberg equilibrium ? i. Name and briefly explain at least one alternative method for correcting the external effect that exists between the players. Explain how the method would work to achieve a Pareto efficient outcome and what effect it would have on the distribution of fish.(Hint: Do not go into the mathematics of the way to correct for the external effect, simply explain it intuitively.)