Need help with this Evironmental Economics Excercise.

Link for DICE manual belowif needed:

http://www.econ.yale.edu/~nordhaus/homepage/homepage/documents/DICE_Manual_100413r1.pdf

Climate change is currently one of the most prominent environmental problem facing today's society. To some, it is an imminent threat that requires immediate and aggressive action, while to others is it an over- hyped concern that may require no action at all. To an environmental economist, the correct course of action requires balancing the tradeoff between the benefits of reduced damages and costs of undertaking abatement activity. To help assess these benefits and costs, economist often rely on simplified models called Integrated Assessment Models (IAMs) linking the economic activities of production and carbon emissions, the physical accumulation of that carbon in the atmosphere and its effect on global temperature, and the economic damages from the rise in temperature. On the most well-known IAMs is the Dynamic Integrated Climate-Economy (DICE) model constructed by William Nordhaus. You will use two simple equations to describe the economic activity-physical response linkage, You will then find the marginal damage function and marginal abatement cost function used by Dr. Nordhaus in the DICE model. After making some simplifying assumptions about the steady-state level of economic activity, you will estimate the economically efficient level of carbon emission control the world should undertake. 1. (16 points) Create a simple model of climate change dynamics. A model of this sort would include an equation for greenhouse gas accumulation, M, and an equation for temperature change, T. Assume that dM/dt = BE(t) - SM(t), and dT/dt = a[AM(t) - T(t)], where M = stock of greenhouse gases (in billions of tons), E = the uncontrolled emission level of carbon (in billions of tons per year), and T= the global temperature increase in Celsius over preindustrial levels). B, 8, a, and I are parameters in this model. a. (2 points) Solve for and report the steady-state relationship of M by setting dM/dt = 0. Report the stock of greenhouse gas emissions, M, as a function of as a function of the emission level of carbon, E. b. (2 points) Solve for the steady-state relationship of T by setting dT/dt =0. Report the equation for global temperature increase, T, as a function of the stock of greenhouse gases, M. C. (2 points) Substitute your equation from 1.a into your equation from 1.b and solve for the implied steady-state relationship of T as a function of E. Report that equation here. d. (2 points) Assume that a=0.02, A=0.003, B=0.5, 8=0.005. Substitute these values into the equation you found for part 1.c. and report the equation of T as a function of E. e. (2 points) Search the web for the most current estimate of global carbon emissions that you can find. (Note: If you find an estimate of current global CO2 emissions, you can convert this to an estimate of carbon emissions by dividing by 3.67.) Report that estimate here. f. (2 points) If the world were to freeze carbon emissions at the level you found in part 1.e, what increase in global temperature would we eventually expect to see, using your equation from part 1.d? g. (2 points) Assume that the steady state uncontrolled level of emissions is 12 billion tons, E=12. What increase in global temperature would we eventually expect to see if none of these emissions are controlled? h. (2 points) What increase in global temperature would we eventually expect to see if 25% of these emissions are controlled? Climate change is currently one of the most prominent environmental problem facing today's society. To some, it is an imminent threat that requires immediate and aggressive action, while to others is it an over- hyped concern that may require no action at all. To an environmental economist, the correct course of action requires balancing the tradeoff between the benefits of reduced damages and costs of undertaking abatement activity. To help assess these benefits and costs, economist often rely on simplified models called Integrated Assessment Models (IAMs) linking the economic activities of production and carbon emissions, the physical accumulation of that carbon in the atmosphere and its effect on global temperature, and the economic damages from the rise in temperature. On the most well-known IAMs is the Dynamic Integrated Climate-Economy (DICE) model constructed by William Nordhaus. You will use two simple equations to describe the economic activity-physical response linkage, You will then find the marginal damage function and marginal abatement cost function used by Dr. Nordhaus in the DICE model. After making some simplifying assumptions about the steady-state level of economic activity, you will estimate the economically efficient level of carbon emission control the world should undertake. 1. (16 points) Create a simple model of climate change dynamics. A model of this sort would include an equation for greenhouse gas accumulation, M, and an equation for temperature change, T. Assume that dM/dt = BE(t) - SM(t), and dT/dt = a[AM(t) - T(t)], where M = stock of greenhouse gases (in billions of tons), E = the uncontrolled emission level of carbon (in billions of tons per year), and T= the global temperature increase in Celsius over preindustrial levels). B, 8, a, and I are parameters in this model. a. (2 points) Solve for and report the steady-state relationship of M by setting dM/dt = 0. Report the stock of greenhouse gas emissions, M, as a function of as a function of the emission level of carbon, E. b. (2 points) Solve for the steady-state relationship of T by setting dT/dt =0. Report the equation for global temperature increase, T, as a function of the stock of greenhouse gases, M. C. (2 points) Substitute your equation from 1.a into your equation from 1.b and solve for the implied steady-state relationship of T as a function of E. Report that equation here. d. (2 points) Assume that a=0.02, A=0.003, B=0.5, 8=0.005. Substitute these values into the equation you found for part 1.c. and report the equation of T as a function of E. e. (2 points) Search the web for the most current estimate of global carbon emissions that you can find. (Note: If you find an estimate of current global CO2 emissions, you can convert this to an estimate of carbon emissions by dividing by 3.67.) Report that estimate here. f. (2 points) If the world were to freeze carbon emissions at the level you found in part 1.e, what increase in global temperature would we eventually expect to see, using your equation from part 1.d? g. (2 points) Assume that the steady state uncontrolled level of emissions is 12 billion tons, E=12. What increase in global temperature would we eventually expect to see if none of these emissions are controlled? h. (2 points) What increase in global temperature would we eventually expect to see if 25% of these emissions are controlled