Economics-QA730

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The Economics of Sustainability and the Environment
 

 

  1. Conduct a cost benefit analysis of climate change under the following scenarios. For each scenario, find the value of the interest rate that would equate the present value of the benefits and costs of mitigation. You are encouraged to use excel, and to calculate costs and benefits for every year in a separate column.

 

  1. The cost of mitigation is a one-time payment of 1$. Damages averted amount to one time value of 100$ in 50 years.
  2. The cost of mitigation is a one-time payment of 1$. Damages averted amount to a value of 100$ per year, for every year between 2050 and 2100.

    3.  

  3. The cost of mitigation is an annual payment of 1$ between 2020 and 2050. Damages averted amount to a value of 100$ per year, for every year between 2050 and 2100.
  4. The cost of mitigation is an annual payment of between 2020 and 2100 which starts off at 1$ per year, but declines at a rate of 0.02 per year. Damages averted amount to an annual value between 2050 and 2100, that starts off at 100$ and increases at a rate of 3% per year.

 

For the following questions, use the formula for calculating an infinite geometric sum.

 

     

  1. Repeat question b but treat damages as perpetual instead of ending at 2100.
  2. Repeat question c but treat both the costs and the damages as perpetual instead of ending at 2050 and 2100.
  3. Repeat question c but treat both the costs and the damages as perpetual instead of ending at 2050 and 2100.

 

  1. In class, we discussed a formula that expresses the discount rate on consumption in terms of three parameters. Name the three parameters, and determine, for each of them, whether increases in the value of the parameter will increase or decrease the discount rate on consumption.
     

    1. I think these are the three parameter
    2. Discount rate on consumption good = discount rate on utility + (curvature of utility function * growth rate of consumption

      3.  
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      • Assess each of the following claims as correct / incorrect
        1. In an economy with a perfect credit market, in equilibrium, the market interest rate equals the discount rate on consumption.

          2.  

        2. The discount rate on consumption and the discount rate on utility (also called the pure or psychological discount rate) are generally equal.
        3. The discount factor between two periods is defined as the factor by which value is discounted between these two periods. The discount factor over a period of 30 years is the annual discount factor taken to the power of 30.

          4.  

        4. In an economy that has a constant level of consumption (no growth, no shrinking) the discount rate on consumption and on utility are equal.
        5. For a person that has a linear utility function (the marginal utility of consumption is constant), the discount rates on consumption and on utility are equal.

          6.  

        6. A person who values utility equally no matter when in time it occurs has a discount rate on utility that equals zero.
        7. A person who values utility equally no matter when in time it occurs, will always agree to trade off 1$ today and 1.01$ in ten years.

          8.  

        8. Even if two people differ in their annual discount rate on utility, these differences will diminish for decisions involving longer and longer time horizons.
        9. It’s easier to measure the discount rate on utility than the discount rate on consumption.

       

      1. Consider an investment opportunity in a project that has a cost C now and a benefit of B in 100 years. Does this investment become more or less attractive if
         

        1. The future expected growth rate of consumption increases
        2. A new asteroid is identified which scientist say has a small probability of colliding with the Earth and ending human life over the next 100 years.

          3.  

        3. Instead of being received all at once in 100 years, the benefits B are distributed evenly (in terms of undiscounted monetary value), year-by-year, over the next 100 years.

       

       

      1. One of the potential damages of climate change is an increase in the chance that people may melt to death. In order to estimate the increase in the rates of melting, econometricians look at historical data on the rates of melting in years that were warmer than average. The results were summarized in the table below. For example, in an average year, the chance of melting was estimated at 0.0001, but in years in which the temperature was 5 degrees higher, it was estimated at 0.001 (0.1%). The last two rows provide the 95% confidence interval of the estimates. For example, in an average year, the chance of melting is somewhere between 0 and 0.0002 with 95%.
           

        1. Why are there error bars on the estimates (refer to the method by which these estimates are derived)?
        2. Another scholar examined a cross section of countries and found that in countries that are generally warmer by the same magnitudes as in the tables, the melting rates are much higher than estimated here. Do you find these estimates more reliable or less than those obtained through the time series analysis?
        3. Why is the error bar on the +5 degree years the highest?

          4.  

        4. Suppose you were instructed to estimate the expected costs of climate change under a scenario in which there is 5 degree warming. With probability 95%, assign the rate of melting to be 0.001. With probability 2.5% assign it to be 0.004, and with probability 2.5% to be zero. What is the expected number of people who are going to melt if the global population will be at 10 billion?

          5.  

        5. Now suppose that some expert claims that there is also a small chance that if the temperature exceeds 5 degree warming, everyone will melt (i.e. the melting rate will be 1). How confident can we be that this is wrong? If we assign this estimate a likelihood of 2.5%, how does that change your answer to (c)? how does this hypothetical simulation reflect Weitzmann’s general argument about uncertainty and fat tails?

          6.  

       

      Change of temperature compared to average year 0 1 2 3 4 5
      Chance of melting 0.0001 0.00011 0.00013 0.00017 0.00023 0.001
      lower error 0.0001 0.00011 0.00013 0.00017 0.00023 0.001
      upper error 0.0001 0.00012 0.00015 0.0002 0.0003 0.003
      min value (95%) 0 0 0 0 0 0
      max value (95%) 0.0002 0.00023 0.00028 0.00037 0.00053 0.004

       

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