Q1: The government has decided to introduce a marketable permit system to address a pollution problem. Currently there are three firms releasing 15 units each of emissions (denoted as E) into the environment for a total of 45 units. Each firm's Abatement costs are as follows Firm 1: TAC = 3A² Firm 2: TAC = A2 Firm 3: TAC = 1.5A² Where A is a unit of abatement such that E 15 - A would be the level of emissions with abatement. The regulator has estimated the aggregate benefit of abatement as B = 90A - A² 1. Find the MAC for each firm and aggregate to get the total MAC for the industry (aggregate horizontally: A1 + A2 + A3 = A). Draw a graph with A on the horizontal axis and carefully graph the MAC 2. Find the marginal benefit of abatement, MB, and add it to your graph from (a) 3. What is the optimal level of Abatement? What would be the permit price for this level of abatement? What would be the aggregate amount of emissions still being produced? If we write the marginal benefit of abatement in term of emission, we get the marginal damage function. 1. If the current emissions (total) are 45 - A = E, then find a simplified expression for the marginal damage function MD = f(E) 2. Similarly, each firm's marginal savings function is found by replacing A₁ = 15 - E; Write out each firm's MAC as a function of E. 3. Aggregate each firm's MAC to get the aggregate MAC function. With E on the horizontal axis, graph the MD and MAC functions. What is the equilibrium value of E? 4. Now suppose the government gives each firm five permits (E = 5) which they can use or trade amongst themselves. Calculate the outcome of the trading market. What will be 1. The permit price? 2. Each firm's E and abatement (A). 3. Who will be net sellers and net buyers of the permits?
Q1: The government has decided to introduce a marketable permit system to address a pollution problem. Currently there are three firms releasing 15 units each of emissions (denoted as E) into the environment for a total of 45 units. Each firm's Abatement costs are as follows Firm 1: TAC = 3A² Firm 2: TAC = A2 Firm 3: TAC = 1.5A² Where A is a unit of abatement such that E 15 - A would be the level of emissions with abatement. The regulator has estimated the aggregate benefit of abatement as B = 90A - A² 1. Find the MAC for each firm and aggregate to get the total MAC for the industry (aggregate horizontally: A1 + A2 + A3 = A). Draw a graph with A on the horizontal axis and carefully graph the MAC 2. Find the marginal benefit of abatement, MB, and add it to your graph from (a) 3. What is the optimal level of Abatement? What would be the permit price for this level of abatement? What would be the aggregate amount of emissions still being produced? If we write the marginal benefit of abatement in term of emission, we get the marginal damage function. 1. If the current emissions (total) are 45 - A = E, then find a simplified expression for the marginal damage function MD = f(E) 2. Similarly, each firm's marginal savings function is found by replacing A₁ = 15 - E; Write out each firm's MAC as a function of E. 3. Aggregate each firm's MAC to get the aggregate MAC function. With E on the horizontal axis, graph the MD and MAC functions. What is the equilibrium value of E? 4. Now suppose the government gives each firm five permits (E = 5) which they can use or trade amongst themselves. Calculate the outcome of the trading market. What will be 1. The permit price? 2. Each firm's E and abatement (A). 3. Who will be net sellers and net buyers of the permits?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Q1: The government has decided to introduce a marketable permit system to address a pollution problem. Currently
there are three firms releasing 15 units each of emissions (denoted as E) into the environment for a total of 45 units.
Each firm's Abatement costs are as follows
Firm 1: TAC = 3A²
Firm 2: TAC = A2 Firm 3: TAC = 1.5A²
Where A is a unit of abatement such that E 15 - A would be the level of emissions with abatement.
The regulator has estimated the aggregate benefit of abatement as B = 90A - A²
1. Find the MAC for each firm and aggregate to get the total MAC for the industry (aggregate horizontally: A1 + A2 +
A3 = A). Draw a graph with A on the horizontal axis and carefully graph the MAC
2. Find the marginal benefit of abatement, MB, and add it to your graph from (a)
3. What is the optimal level of Abatement? What would be the permit price for this level of abatement? What would
be the aggregate amount of emissions still being produced?
If we write the marginal benefit of abatement in term of emission, we get the marginal damage function.
1. If the current emissions (total) are 45 - A = E, then find a simplified expression for the marginal damage function MD
= f(E)
2. Similarly, each firm's marginal savings function is found by replacing A₁ = 15 - E; Write out each firm's MAC as a
function of E.
3. Aggregate each firm's MAC to get the aggregate MAC function. With E on the horizontal axis, graph the MD and
MAC functions. What is the equilibrium value of E?
4. Now suppose the government gives each firm five permits (E = 5) which they can use or trade amongst themselves.
Calculate the outcome of the trading market. What will be
1. The permit price?
2. Each firm's E and abatement (A).
3. Who will be net sellers and net buyers of the permits?
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