Recall the permit trading game played in class. The nine firms Amazon, Apple, Bayer, Exxon Mobil, Google, Microsoft, Monsanto, Unilever and DuPont had marginal abatement cost of 2,3,...9,10, respectively. A total of nine pollution permits were distributed to the firms. Each firm produces two units of output and while doing so, also produces to units of pollution. a) In Periods 3-5, each firm was originally given one pollution permit. In Period 4, the following trades were made: Unilever buys a permit from Amazon for $8, Microsoft buys a permit from Apple for $7 and DuPont buys one from Bayer for $7. Are there any additional trades that would be an improvement in economic efficiency (i.e. increase the sum of profits of all firms, i.e. the overall size of the pie)? Are there any additional trades that could have been made that would provide a Pareto improvement (i.e. each firm's profit is weakly higher and the profit of at least one firm is strictly higher)? b) In Period 6, Amazon, Apple, Bayer, Exxon Mobil each got two permits, Google got one and the other companies got zero permits. The following trades occurred each for $7: Unilever buy one permit from Apple and one from Amazon, Microsoft buys one permit from Bayer and one from Apple, Monsanto buy one permit from Exxon Mobile and one from Amazon, and Dupont buys one permit from Bayer. Are there any additional trades that would be an improvement in economic efficiency? Are there any additional trades that could have been made that would provide a Pareto improvement? c) Assuming that all firms are rational, argue why, in general, the initial distribution of the permits should not matter for the resulting sum of profits of all firms after permit trading has finalized.