Increases in carbon dioxide in the Earth's atmosphere have been cited as a probable cause of global warming. Let y represent the stock of carbon dioxide and let x > 0 (a constant) represent the flow of carbon dioxide emissions that come from industrial activity. Assume that the dynamics of y are given by y=x-y^a, where the term y^a represents the Earth's capacity to remove carbon dioxide from the atmosphere and allow its absorption elsewhere (i.e., in trees and oceans). (a) (2) Find the steady-state of stock of carbon dioxide. (b) (4) Suppose a > 0, show the steady-state in a phase diagram. Is the steady-state stable? (c) (4) Now suppose a < 0, show the steady-state in a phase diagram. Is the steady-state stable?

Increases in carbon dioxide in the Earth's atmosphere have been cited as a probable cause of global warming. Let y represent the stock of carbon dioxide and let x > 0 (a constant) represent the flow of carbon dioxide emissions that come from industrial activity. Assume that the dynamics of y are given by y=x-y^a, where the term y^a represents the Earth's capacity to remove carbon dioxide from the atmosphere and allow its absorption elsewhere (i.e., in trees and oceans). (a) (2) Find the steady-state of stock of carbon dioxide. (b) (4) Suppose a > 0, show the steady-state in a phase diagram. Is the steady-state stable? (c) (4) Now suppose a < 0, show the steady-state in a phase diagram. Is the steady-state stable?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.5P

See similar textbooks

Similar questions

In what ways (it) company investments in research and development create positive externalities?
What is the difference between a positive and a normative statement?
What is an example of a problem in the world today, not mentioned in the chapter, that has an economic dimension?
Consider two ways of protecting elephants from poachers in African countries. In one approach, the government sets up enormous national parks that have sufficient habitat for elephants to thrive and forbids all local people to enter the parks or to injure either the elephants or their habitat in any way. In a second approach, the government sets up national parks and designates 10 villages around the edges of the park as official tourist centers that become places where tourists can stay and bases for guided tours inside the national park. Consider the different incentives of local villagers-who often are very poor-in each of these plans. Which plan seems more likely to help the elephant population?
What are four responses to the claim that people should not behave in the way described in this chapter?
Consider two approaches to reducing emissions of CO2 into the environment from manufacturing industries in the United States. In the first approach, the U.S. government makes it a policy to use only predetermined technologies. In the second approach, the U.S. government determines which technologies are cleaner and subsidizes their use. Of the two approaches, which is the command-and-control policy?
What are the similarities between a consumers budget constraint and societys production possibilities frontier, not just graphically but analytically?
What assumptions about the economy must he true for the invisible hand to work? To what extent are those assumptions valid in line real world?
What does a point inside the production possibility frontier represent?
What are three reasons to study economics?
Becky and Sarah are sisters 1who share a room. Their room can easily get messy, and their parents am always telling them to tidy it. Here are the costs and benefits to both Becky and Sarah, of taking the time to clean their room: If both Becky and Sarah clean, they each spends two hours and get a clean room. If Becky decides not to clean and Sarah does all the cleaning, then Sarah spends 10 hours cleaning (Becky spends 0) but Sarah is exhausted. The same would occur for Becky if Sarah decided not to cleanâ€”Becky spends 10 hours and becomes exhausted. If both girls decide not to clean, they both have a dirty room. What is the best outcome for Becky and Sarah? What is the worst outcome? (It would help you to construct a prisoners dilemma table.) Unfortunately, we know that the optimal outcome will most liker not happen, and that the sisters probably will choose the worst one instead. Explain what it is about Beckys and Sarahs reasoning that will lead them both to choose the worst outcome.
Why is a production possibilities frontier typically drawn as a curve, rather than a straight line?