*8. Carbon dioxide is well known as the most significant greenhouse gas, leading to cli- mate change and global warming. But other gases are also greenhouse gases contrib- uting to global warming and thus appropriate to regulate in controlling the problem. One of these is methane (uncombusted natural gas). Methane and Co, differ in how a kilogram in the atmosphere affects warming, and they also differ in how quickly the gases leave the atmosphere. Although we are oversimplifying the physical science, assume that after a kilogram of methane or Co, are emitted into the atmosphere, they decay expo- nentially, with half of the Co, disappearing in 100 years and half of the methane disappearing in 10 years. Although methane disappears quickly, while it is in the atmosphere it is more problematic for global warming in the sense that a kilogram of methane in the atmosphere causes approximately 25 times the warming as a kilogram of Co, For the questions below, assume a discount rate of 5% per year. a. For each gas, graph the stock of gas remaining in the atmosphere following the injection of 1 ton into the atmosphere. You can put the two lines on the same graph. Take your graph out at least 100 years. (Hint: if s = pat and the stock declines from 1 to when t goes from zero to the half-life, one can calculate a for each gas.). What is the persistence rate for each gas? (Hint: use the continuous time version of Eq. 14.24; see problem 5.) b. You are advising the EPA on what emission tax to place on methane and Co, Assume first of all that the marginal damage from a ton of CO, in the atmo- sphere is $1 per year per ton and it is constant over time, and independent of the stock of greenhouse gases in the atmosphere. What would be the ratio of the tax on methane to the tax on CO, using efficiency as your guide in setting taxes? c. How would your answer to (b) change if you only considered a horizon of 10 years? Of 50 years? Of 100 years? (One hundred years is the figure the Kyoto Protocol uses to consider trade-offs between methane and CO,1 d. How would your answer to (b) change if marginal damage from a ton of CO, increased at the rate of 1% per year? e. Compare your answers to (c) and (d). *8. Carbon dioxide is well known as the most significant greenhouse gas, leading to cli- mate change and global warming. But other gases are also greenhouse gases contrib- uting to global warming and thus appropriate to regulate in controlling the problem. One of these is methane (uncombusted natural gas). Methane and Co, differ in how a kilogram in the atmosphere affects warming, and they also differ in how quickly the gases leave the atmosphere. Although we are oversimplifying the physical science, assume that after a kilogram of methane or Co, are emitted into the atmosphere, they decay expo- nentially, with half of the Co, disappearing in 100 years and half of the methane disappearing in 10 years. Although methane disappears quickly, while it is in the atmosphere it is more problematic for global warming in the sense that a kilogram of methane in the atmosphere causes approximately 25 times the warming as a kilogram of Co, For the questions below, assume a discount rate of 5% per year. a. For each gas, graph the stock of gas remaining in the atmosphere following the injection of 1 ton into the atmosphere. You can put the two lines on the same graph. Take your graph out at least 100 years. (Hint: if s = pat and the stock declines from 1 to when t goes from zero to the half-life, one can calculate a for each gas.). What is the persistence rate for each gas? (Hint: use the continuous time version of Eq. 14.24; see problem 5.) b. You are advising the EPA on what emission tax to place on methane and Co, Assume first of all that the marginal damage from a ton of CO, in the atmo- sphere is $1 per year per ton and it is constant over time, and independent of the stock of greenhouse gases in the atmosphere. What would be the ratio of the tax on methane to the tax on CO, using efficiency as your guide in setting taxes? c. How would your answer to (b) change if you only considered a horizon of 10 years? Of 50 years? Of 100 years? (One hundred years is the figure the Kyoto Protocol uses to consider trade-offs between methane and CO,1 d. How would your answer to (b) change if marginal damage from a ton of CO, increased at the rate of 1% per year? e. Compare your answers to (c) and (d)
