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## Consider Weitzman-Gollier discounting method. In particular, suppose we face $1 trillion in real dollars worth of damages in 100 years. The real rates of economic growth over this time period are estimated to be: 0.5% with probability ¼; 1% with probability ¼; 3% with probability ¼; and 5% with probability ¼. Please answer the following questions (spreadsheet on Canvas and notes may be of help here): What is the expected real rate of economic growth? What is the present value of future damages using the expected growth rate? What is the expected discount factor? What is the present value of future damages using the expected discount factor? What is the implied rate of discounting, based on your answer to (d)?

- Common pool resources are characterized by non-excludability and rivalry in consumption. Explain what this means

- Consider a particular type of a public good (a public “bad”): a global negative externality (think climate change). Suppose a person derives a (private) marginal benefit of $50 from emitting 1 ton of carbon dioxide. This emission, however, hurts
*everyone*on the planet in the amount of $0.0000001. If a person acts in a way to maximize his own personal benefit, will he emit this ton of carbon dioxide? Explain.

- Traditional (exponential) discounting. Using a spreadsheet program, graph the changes in the present value of 1 billion dollars over time. Use a one year step, starting at year t=0 (today) up to year t=99. Set up a table of the following format, and compute the present values under different assumptions about the discount rate. Put time on the horizontal axis, the present values on the vertical axis, and graph all the present value curves on the same graph (we have 3 different discount rates, so you should have 3 curves on the graph).

t | PV using r=0.01 | PV using r=0.05 | PV using r=0.1 |

0 | 1000000000 | 1000000000 | 1000000000 |

1 | |||

2 | |||

… | |||

99 |

What is the present value of 1 billion dollars at t=99 (i.e., in one hundred years)? Discuss the importance of the choice of a discount rate for evaluating, for example, environmental damages removed into a fairly distant future.

- (US Wetland Valuation exercise). Consider the TEEB ecosystem services valuation database (http://www.teebweb.org/publication/tthe-economics-of-ecosystems-and-biodiversity-valuation-database-manual ). Open the Excel spreadsheet, and filter results to find the “Inland Wetlands” Biome, then go to the Country field and select the United States. Your task is to make sense of the information and construct an estimate of the value of all ecosystem services (let’s make it equivalent to the Total Economic Value (TEV)) from an inland wetland. After the initial query, you should see

and

Please note a few things. First, observe that a few estimates are based on the same Thibodeau et al. (1981) study, and that one of the values they report is already a TEV. So, use that value as one data point in your estimate of TEV of wetlands. Second, different studies show values for different ecosystem services (use ESsubservice for classification here), and some ecosystem services (like “Flood prevention”) are valued by more than one study. Therefore, before you aggregate values for different ecosystem services, you may want to average the values for a particular service across different studies to avoid double-counting. Also remember that once you aggregate values for different ecosystem services, you will have one estimate of TEV, and you already have another one from Thibodeau et al. So you need to deal with this fact. Third, the values reported are in dollars per ha per year but the year is different, so you’ll want to adjust your values to the same year *before *any aggregation occurs. To do that, a reasonable way to proceed is to do an adjustment for the purchasing power of a dollar (adjustment for inflation). You can do that in Excel using hints from http://www.maa.org/press/periodicals/loci/joma/the-consumer-price-index-and-inflation-adjust-numbers-for-inflation or you can just use the calculator here http://www.bls.gov/data/inflation_calculator.htm since you only have a few data points. Please adjust all dollar values to 2015 dollars.

After addressing all the issues above, you should be able to report your estimate of an average TEV of an inland wetland in USA in 2015 dollars per ha per year. Using a real discount rate of 3%, what is the value of 1 ha of wetland as a unit of (perpetually lived) natural capital?

Please prepare a spreadsheet to support your conclusions and turn in it along with your write-up. Upon completion of this problem, please comment on the reliability of the estimate, especially how it might relate to the number of valuation studies.

- Consider Weitzman-Gollier discounting method. In particular, suppose we face $1 trillion in real dollars worth of damages in 100 years. The real rates of economic growth over this time period are estimated to be: 0.5% with probability ¼; 1% with probability ¼; 3% with probability ¼; and 5% with probability ¼. Please answer the following questions (spreadsheet on Canvas and notes may be of help here):
- What is the expected real rate of economic growth?
- What is the present value of future damages using the expected growth rate?
- What is the expected discount factor?
- What is the present value of future damages using the expected discount factor?
- What is the implied rate of discounting, based on your answer to (d)?