Question $4($worth $23$ points$)$

a$)$ Please explain why marginal benefits of emissions being equalized across all firms is a necessary condition for permit trading equilibrium. $[$Two sentences.$](3$ points$)$

b$)$ What other condition needs to hold in permit trading equilibrium? $[$One sentence.$](1$ point$)$

For the remainder of this question, suppose that two firms $($labeled $$I$$ and $$II$)$ operate in an industry that generates pollution emissions, e$.$ Specifically, the firms use a polluting production process that generates the following marginal benefits of emissions, depending on firm type:$$

MBI $=8$ e$$

MBII $=123/2$ e$.$

c$)$ Plot the relevant marginal benefit of emissions schedules of the two firms on the same diagram in the space below, and label your diagram clearly. $[$Hint: your diagram should have pollution emissions at the firm level, e$,$ on the horizontal axis and $ amounts on the vertical axis.$](4$ points$)$

d$)$ In the absence of any regulation, what emissions levels will each type of firm produce, and why? $(1$ point$)$

For the remainder of this question, a government regulator decides to try and limit pollution.$$

e$)$ Suppose initially that the regulator introduces a uniform standard, limiting all firms to $4$ units of emissions, regardless of type. Calculate the total abatement costs for each firm associated with the move from no regulation to regulation. $[$Hint $1$: you will need to know what abatement costs are. Recall that $$to abate$$ means $$to cut back,$$ so abatement costs are the costs associated with cutting back emissions.$][$Hint $2$: abatement costs have a very clear graphical representation in this instance, if you refer back to the graph you drew above.$](4$ points$)$

Now suppose the regulator introduces a permit trading scheme in a bid to reduce industry pollution. Under the scheme, each firm is initially allocated $4$ permits $($one for each unit of emissions$),$ which firms can then subsequently trade among themselves. $5$

f$)$ Which firm is likely to sell permits and which firm is likely to buy permits, and why? $[$Two sentences.$](4$ points$)$

g$)$ Suppose firms take the equilibrium permit price as given, then buy or sell $($as they see fit$)$ at that price. Could a price equal to $5$ be an equilibrium permit price in this instance? Please show any relevant calculations. $(6$ points$)$