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*2. A very simple version of the normative model described in the text involves a simple economic growth process converging to a steady-state, where values do not change over time." A simple model of the climate would involve a greenhouse gas accumulation equa- tion and a temperature change equation: d/dt =B E(t) - 8 M(t) and dT/dt=a [M(t)- T(t)] where M is the stock of greenhouse gases (in billions of tons), E(t) is the emission level (in billions of tons per year) and T(t) is the global temperature increase in C over preindustrial levels), with values of B, 8, a, and 1 of 0.50, 0.005, 0.02, and 0.003, respectively. Note that in 2005 world GDP was about $60 trillion and approximately 8 billion tons of carbon were emitted (in the form of carbon dioxide equivalent). a. Using the simple climate model, what is the relationship between the steady-state emission level (E+) and the steady-state temperature (T*)? Recall that steady-state means that neither M nor T are changing. b. Convert Figure 2.2 into a plot of the damage as a function of temperature change, assuming steady-state global GDP of US$100 trillion per year. Generate a plot of the marginal damage ($ per degree temperature increase) as a function of the temperature rise. c. Use the results from parts (a) and (b) to generate a plot showing the marginal damage ($ per ton of carbon emissions) as a function of the fraction of emissions controlled (assume steady-state uncontrolled emissions of 12 billions tons of carbon). d. What level of emission control balances the marginal cost of control with the marginal damage? *2. A very simple version of the normative model described in the text involves a simple economic growth process converging to a steady-state, where values do not change over time." A simple model of the climate would involve a greenhouse gas accumulation equa- tion and a temperature change equation: d/dt =B E(t) - 8 M(t) and dT/dt=a [M(t)- T(t)] where M is the stock of greenhouse gases (in billions of tons), E(t) is the emission level (in billions of tons per year) and T(t) is the global temperature increase in C over preindustrial levels), with values of B, 8, a, and 1 of 0.50, 0.005, 0.02, and 0.003, respectively. Note that in 2005 world GDP was about $60 trillion and approximately 8 billion tons of carbon were emitted (in the form of carbon dioxide equivalent). a. Using the simple climate model, what is the relationship between the steady-state emission level (E+) and the steady-state temperature (T*)? Recall that steady-state means that neither M nor T are changing. b. Convert Figure 2.2 into a plot of the damage as a function of temperature change, assuming steady-state global GDP of US$100 trillion per year. Generate a plot of the marginal damage ($ per degree temperature increase) as a function of the temperature rise. c. Use the results from parts (a) and (b) to generate a plot showing the marginal damage ($ per ton of carbon emissions) as a function of the fraction of emissions controlled (assume steady-state uncontrolled emissions of 12 billions tons of carbon). d. What level of emission control balances the marginal cost of control with the marginal damage