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What motivates a firm decision to buy or sell a permit in the market? How can I Show graphically that firms with different marginal abatement

What motivates a firm decision to buy or sell a permit in the market? How can I Show graphically that firms with different marginal abatement costs can profitably trade. Why might this approach be better than a uniform Pigovian tax?

How can I make a diagram in the emissions (x-axis) and dollars (y-axis) space with two firms whose marginal abatement costs differ. Both firms have the same total capacity for emissions. Firm A starts with lower marginal abatement costs than Firm B, but they begin to increase more rapidly than Firm B's and cross above them at the halfway point to zero emissions. (You can assume Firm B's marginal abatement costs are a straight line). If the emissions restriction (a vertical line on the graph) is to the right of the crossing point, who is the buyer of permits? Who is the seller? Can you identify the gains from trade?

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