5. (12 points total) Consider two firms with the following marginal abatement costs (MAC) as a
function of emissions
(E): MAC_1 = 11 - 2E_1
MAC_2 = 8.5 - E_2,
and assume marginal external damages (MED) from the aggregate emissions of both firms
(E_Agg = E_1 + E_2) is: MED = .5E_Agg.
a. (3 points) What is the socially efficient level of aggregate emissions (E*_Agg)? Explain your
answer.
b. (3 points) Suppose the government decided to reach E*_Agg through a tax on emissions.
What tax per unit of emissions would the government need to impose? How will this affect the
profits of the two firms? (remember to include both the tax payments and abatement costs the
firms incur). Explain your answer.
(3 points) Suppose instead the government decided to reach E*_Agg through a subsidy to
abatement. What subsidy per unit of abatement would the government need to impose? How will
this affect the profits of the two firms? Explain your answer.
d. (3 points) Will society as a whole be better or worse off in one or the other of the two
scenarios above (tax vs subsidy)? Explain your answer.
(3 points) Suppose instead the government decided to reach E*_Agg through a subsidy to
abatement. What subsidy per unit of abatement would the government need to impose? How will
this affect the profits of the two firms? Explain your answer.
d. (3 points) Will society as a whole be better or worse off in one or the other of the two
scenarios above (tax vs subsidy)? Explain your answer..
5. (12 points total) Consider two firms with the following marginal .pdf
1. 5. (12 points total) Consider two firms with the following marginal abatement costs (MAC) as a
function of emissions
(E): MAC_1 = 11 - 2E_1
MAC_2 = 8.5 - E_2,
and assume marginal external damages (MED) from the aggregate emissions of both firms
(E_Agg = E_1 + E_2) is: MED = .5E_Agg.
a. (3 points) What is the socially efficient level of aggregate emissions (E*_Agg)? Explain your
answer.
b. (3 points) Suppose the government decided to reach E*_Agg through a tax on emissions.
What tax per unit of emissions would the government need to impose? How will this affect the
profits of the two firms? (remember to include both the tax payments and abatement costs the
firms incur). Explain your answer.
(3 points) Suppose instead the government decided to reach E*_Agg through a subsidy to
abatement. What subsidy per unit of abatement would the government need to impose? How will
this affect the profits of the two firms? Explain your answer.
d. (3 points) Will society as a whole be better or worse off in one or the other of the two
scenarios above (tax vs subsidy)? Explain your answer.
(3 points) Suppose instead the government decided to reach E*_Agg through a subsidy to
abatement. What subsidy per unit of abatement would the government need to impose? How will
this affect the profits of the two firms? Explain your answer.
d. (3 points) Will society as a whole be better or worse off in one or the other of the two
scenarios above (tax vs subsidy)? Explain your answer.
