Consider two energy-producing firms that generate greenhouse gases. The firms have different (heterogencous) costs associated with reducing (abating) their emissions. Let one firm have high costs (H) while the other has low costs (L). Since taking action to reduce greenhouse gas emissions is costly, the firms will choose a quantity of abatement of zero units if left to their own choices: qL=qH=0. The total cost of abatement for Firm H is cH(qH)=45qH2. The total cost of abatement for Firm L is cL(qL)=32qL2. Assume that the marginal damages (MD) of emissions are valued at $100 per ton. It doesn't matter which firm abates, the benefit is still the same. Total benefits are expressed as 100q=100(qH+qL). 2.1 The Social Planner The role of a social planner is to maximize net benefits for society. This is done by considering the entire economic system and setting marginal costs equal to marginal benefits. The avoided damages of greenhouse gases are considered a benefit. Meanwhile, the fact that it is costly for firms to engage in abatement behaviors means that they will generate costs. The social planner's problem is to choose qL and qH to maximize SocialNetBenefits($)=100qH100qL45qH232qL2 Q12) (2 points) Take the first derivative of equation (5) with respect to qH, set it equal to zero, and solve for the optimal amount of abatement to be completed by Firm H,qH. Q13) (2 points) What is the marginal abatement cost to Firm H of abating quantity qH ? Hint: take the first derivative of the cost function for Firm H first. Q14) (2 points) What is the total abatement cost for Firm H of abating quantity qH ? Q15) (2 points) Take the first derivative of equation (5) with respect to qL, set it equal to zero, and solve for the optimal amount of abatement to be completed by Firm L, qL. Q16) (2 points) What is the marginal abatement cost to Firm H of abating quantity qL ? Hint: take the first derivative of the cost function for Firm L first. Q17) (2 points) What is the total abatement cost for Firm H of abating quantity qL ?.

1. Consider two energy-producing firms that generate greenhouse gases. The firms have different
(heterogencous) costs associated with reducing (abating) their emissions. Let one firm have high
costs (H) while the other has low costs (L). Since taking action to reduce greenhouse gas
emissions is costly, the firms will choose a quantity of abatement of zero units if left to their own
choices: qL=qH=0. The total cost of abatement for Firm H is cH(qH)=45qH2. The total cost of
abatement for Firm L is cL(qL)=32qL2. Assume that the marginal damages (MD) of emissions
are valued at $100 per ton. It doesn't matter which firm abates, the benefit is still the same. Total
benefits are expressed as 100q=100(qH+qL). 2.1 The Social Planner The role of a social planner
is to maximize net benefits for society. This is done by considering the entire economic system
and setting marginal costs equal to marginal benefits. The avoided damages of greenhouse gases
are considered a benefit. Meanwhile, the fact that it is costly for firms to engage in abatement
behaviors means that they will generate costs. The social planner's problem is to choose qL and
qH to maximize SocialNetBenefits($)=100qH100qL45qH232qL2 Q12) (2 points) Take the first
derivative of equation (5) with respect to qH, set it equal to zero, and solve for the optimal
amount of abatement to be completed by Firm H,qH. Q13) (2 points) What is the marginal
abatement cost to Firm H of abating quantity qH ? Hint: take the first derivative of the cost
function for Firm H first. Q14) (2 points) What is the total abatement cost for Firm H of abating
quantity qH ? Q15) (2 points) Take the first derivative of equation (5) with respect to qL, set it
equal to zero, and solve for the optimal amount of abatement to be completed by Firm L, qL.
Q16) (2 points) What is the marginal abatement cost to Firm H of abating quantity qL ? Hint:
take the first derivative of the cost function for Firm L first. Q17) (2 points) What is the total
abatement cost for Firm H of abating quantity qL ?