Comparing costs and benefits in climate change modelsDecember 5The basic point• Costs of reducing emissions, and the costs of climate change, occur to people in different locations and at different points in time.• Abatement costs are likely to fall on people in the near term, in richer countries.• Costs of climate change are likely to fall most heavily on poorer people, in the (possibly distant) future.• A cost-benefit analysis of abatement effort requires that we make these costs comparable.Comparing costs over different income groups• “Decreasing marginal utility of income” says that an extra dollar is worth less to a rich person than to a poor person. Compare the magnitudes “a” and “b”.incomeutilityabWeighting costs for different income groups• Suppose that one dollar is worth 50% more to a poor person than to a rich person.• Suppose that a “project” (e.g. reducing CO2 concentration) costs the rich 1 unit of income (e.g. $100 billion).• By how much (x) does the project have to increase poor income by (e.g. by avoiding costs that they incur from climate change) for the project to increase welfare?• Answer: x(1.5)>1, i.e. x>.66• I multiplied x (the savings to the poor) by 1.5 because (by assumption) one unit of income for rich is worth 1.5 units of income to poor.Discussion of example• This example says that the project increases aggregate utility if it saves the poor at least .66 units of income.• I used the “price” 1.5 to convert units of “income to poor” into “income to rich”.• (We use prices all the time to make the values of different goods – apples and oranges –commensurable.)• Practical significance: In the Stern report, weighting the income of the poor more heavily leads to an increase from 15% to 20% of the estimate of value of annual reduction in gross world product, due to concentration of 550 ppm of GHG.Effects of giving higher weight to income of poor• Since climate change is more likely to harm the poor than the rich, increasing the weight given to the poor (in the cost benefit analysis) increases the estimated cost of climate change.• This weighting scheme leads to an increase in the recommended level of abatement (and the costs of abatement) that society should be willing to incur.Arguments for and against this kind of weighting• Pro: It reflects a reasonable ethical judgment.• Con: (i) The weights are very subjective. You can get “any kind of answer” by choice of weights. This subjective element reduces the value of the exercise.• Con: (ii) Climate change policy is an inefficient means of transferring income. We have more efficient methods of transferring income.Elaborate on efficiency argument• Suppose (using my example above) that the project costs the rich 1 unit of income and increases the income of the poor by 0.8 units. This project increases world welfare, because 1.5(0.8)>1.• However, both the rich and the poor would be better off if the rich simply gave the poor 0.9 units of income, rather than undertaking the project.• The same logic holds whenever the project increases income of poor by less than 1 unit of income.• Thus, the test for efficiency of the project is not related to the weight we give to the income of the poor.More on the efficiency argument• The basic point of the argument against using different weights on income of rich and poor is that doing so encourages viewing climate change policy as a means of redressing income inequality.• Climate change policy should be “targeted” to the problem of climate change, not to the problem of unfair income distribution. Climate change policy would be a very “leaky bucket” if it were used to transfer income.Two examples of costs and benefits of climate change policy.7(1.05).7.0benefits101costsTotalpoorrich.7 (0.9).4.3benefits101Coststotalpoorrich•Number in ( ) shows weighted benefits as in example.•If we use equal weights for the rich and the poor benefits, neither of these projects should be undertaken.•If we weight the poor benefits by 1.5 of rich benefits (as in my example), the first but not the second project should be undertaken.Comparing costs and benefits over time• Discuss above considered whether costs and benefits for different income groups should be weighted equally.• Now I want to consider how to “add up” costs and benefits that occur at different points in time.• In order to do this, we use a discount factor.Discount rates and discount factors• If I face an annual interest rate of 5%, I am indifferent between $0.9524 today and $1 in one year: investing $0.9524 for one year gives me (1.05)0.9524=1.• If I face an annual interest rate of r%, I am indifferent between 1/(1.0+.0r) today and $1 in one year.• (The numerical value of a discount rate of 5% is .05, so the numerical value of a discount rate of r% is .0r.)• 1/(1+.0r) is the one year discount factor corresponding to a one year interest rate (also called the “discount rate”) of r%.• The discount factor is the “price” today of one dollar in one year.• A larger discount rate translates to a smaller discount factor.The “tyranny” of compound discounting• The “price” today of one dollar n years from now is 1/(1+.0r)**n. (1/(1+.0r)) raised to the n)• This is the amount that I would be willing to pay today (e.g. in order to reduce GHG emissions) to avoid having to pay $1 (e.g., resulting from climate change) n years from now.• Table shows amount we would pay today to avoid $100 in damages at different future times.$0.0009$0.296% discount rate$0.27$5.23% discount rate200 years from now100 years from now• With a non-negligible discount rate, we would not spend much to avoid damages in the distant futureThe social discount rate• The social discount rate is used to compare costs and benefits at different points in time for a public project (such as climate change policy).• It is analogous to the private discount rate (or interest rate), except that it reflects society’s preferences and opportunity costs, rather than the individual’s.• If the annual social discount rate is r, the discount factor for n years in the future (the “price” today of one dollar of income n years in the future) is 1/(1+.0r)**n. (“**” means “raised to the n”)The components of the social discount rate• The social discount rate equals:(pure rate of time preference) + (elasticity of marginal utility
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