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

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