Question

Two firms can control emissions at the following marginal costs: MC1=$3q1, mc2=$12q2 where q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms. Assume that with no control at all, each firm would be emitting 100 tons of emissions, or a total of 200 units for both firms.Suppose a control authority decides a total reduction of 60 units of emissions is necessary. It also decides that reduction will be divided equally among each firm. Compute the total cost to society of the reduction strategy 

          Two firms can control emissions at the following marginal costs: MC1=$3q1, mc2=$12q2 where  q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms.  Assume that with no control at all, each firm would be emitting 100 tons of emissions, or a total of 200 units for both firms.Suppose a control authority decides a total reduction of 60 units of emissions is necessary.  It also decides that reduction will be divided equally among each firm. Compute the total cost to society of the reduction strategy
Show more…

Added by Jennifer C.

Principles of Economics
Principles of Economics
Gregory Mankiw 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Two firms can control emissions at the following marginal costs: MC1=$3q1, mc2=$12q2 where q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms. Assume that with no control at all, each firm would be emitting 100 tons of emissions, or a total of 200 units for both firms.Suppose a control authority decides a total reduction of 60 units of emissions is necessary. It also decides that reduction will be divided equally among each firm. Compute the total cost to society of the reduction strategy
Close icon
Play audio
Feedback
Powered by NumerAI
Jennifer Stoner David Collins
Kathleen Carty verified

Andrew Davis and 85 other subject Microeconomics educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
the-cost-of-controlling-emissions-at-a-firm-rises-rapidly-as-the-amount-of-emissions-reduced-increaseshere-is-a-possible-model-cq520040g2-where-g-is-the-reduction-in-emissionsin-pounds-of-po-52788

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model: C(q) = 5200 + 40q^2 where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. Government will pay subsides in the amount of $500 per pound for each pound of pollutant removed (q). For example, if you can remove q=3 pounds of pollutant, you will receive a subsidy of $500*3. How many pounds of pollutant should the firm remove each day in order to minimize Net Cost (Cost minus subsidy)? Your Answer:

Andrew D.
there-are-two-firms-that-emit-so2-as-part-of-their-production-process-firm-1-has-marginal-costs-of-abatement-of-mcx13x1-where-x1-is-measured-in-units-of-abatement-for-firm-1-firm-2-has-margi-82823

There are two firms that emit SO2 as part of their production process. Firm 1 has marginal costs of abatement of MC(x1) = 3x1, where x1 is measured in units of abatement for firm 1. Firm 2 has marginal costs of abatement of MC(x2) = 3x2, where x2 is measured in units of abatement for firm 2. Firm 1 initially emits 60 units of pollution. Firm 2 initially emits 40 units of pollution. The marginal benefit curve is given by: MB(x) = 100 - x, where x is measured in units of pollution abatement in the region. By how much are total abatement costs (over all firms) reduced by allowing firms to buy and sell pollution rights?... referring to the government allowing the companies to buy and sell permits vs allowing equal amounts of pollution.

Madhur L.
the-cost-of-controlling-emissions-at-a-firm-is-given-by-cq4000100-q2-where-q-is-the-reduction-in-emi

The cost of controlling emissions at a firm is given by $$C(q)=4,000+100 q^{2}$$ where $q$ is the reduction in emissions (in pounds of pollutant per day) and $C$ is the daily cost to the firm (in dollars) of this reduction. Government clean-air subsidies amount to $$\$ 500$$ per pound of pollutant removed. How many pounds of pollutant should the firm remove each day in order to minimize $n e t$ cost (cost minus subsidy)?

Finite Mathematics and Applied Calculus

Further Applications of the Derivative

Applications of Maxima and Minima
*

Recommended Textbooks

-
Principles of Economics

Principles of Economics

Gregory Mankiw 8th Edition
achievement 1,887 solutions
Principles of Microeconomics for AP® Courses

Principles of Microeconomics for AP® Courses

Steven A. Greenlaw, David Shapiro, Timothy Taylor 2nd Edition
achievement 1,503 solutions
Economics

Economics

Michael Parkin 12th Edition
achievement 1,333 solutions
*

Transcript

-
00:01 So here we have an optimization problem.
00:02 And the key is, if you look at the very last line of the question, you want to minimize net cost.
00:10 And that net cost is equal to the cost minus the subsidy.
00:15 So let's fill that function out.
00:17 We want to minimize cost and we have a cost function which is 5200 plus 40q squared minus the subsidy.
00:26 Well, the subsidy is 500 times q, right? if you look at that 500 times q, you can see it's 500 times q.
00:33 So we want to minimize this function and to do it, we need to take the derivative with respect to q, right? if you think of this function as looking something like, the other way around, we are looking for the point where the slope is equal to zero because the slope equals to zero is where the minimum is...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever