Economists use climate-economy models (called "integrated assessment models", IAMS), to provide policy makers with advice regarding how fast to abate emissions and what carbon prices to set. This involves weighing the costs of abatement (earlier in time) with the benefits of abatement, damage reduction (later in time). A common objective is to maximize "Welfare (W), which is the sum of happiness (called utility) over time. Different planners discount utility per capita (p) at different rates and make different assumptions regarding their tolerance for intergenerational inequality and the growth rate of per capita consumption (g). These assumptions affect the social discount rate (SDR), which can be thought of as a social real interest rate. a) Social discount rates can be estimated based on Ramsey's Rule, which is: SDR = p + a g p is the discount rate on per capita utility (also called pure rate of time preference) a is the tolerance for inequality between generations where a larger alpha means less tolerance for intergenerational inequality. g is the growth rate of the economy in terms of per capita consumption. * means multiply.
Suppose the economists below use the following values for the Ramsey equation parameters
Analyst Analyst 2 Analyst 3 (Stern) (Nordhaus) (Malthus) 1.35 1.35 .001 .015 .01 .05 -0.015 SDR a) Use Ramsey Rule to calculate each analyst's social discount rate and fill in the table above and redraw in your assignment
b) Use the social discount rates to calculate the respective social discount factors, SDF, where SDF- 1/(1+SDR). To simplify, assume only three time periods-in practice, there are many. Assume there is no inflation and discount rates are "real" vs. "nominal".
c) Assume that current values of net abatement costs in 2020 are estimated to be $12 trillion for a damage reduction net benefit of $37 trillion in 2050 and $74 trillion in 2100. Draw a time line and indicate the current value of the change in social surplus for each date.
d) Underneath the current value, for each economist's choice of discount rates, calculate and write down the present value of the change in total social surplus for that period.
e) For each economist, sum the changes in total social surplus across time periods to calculate the Net Present Value (NPV) of abatement and use this to decide whether each economist would recommend abatement and briefly explain.
f) If the SDR is low, current abatement costs receive (high, low) weight in comparison to future damages reduced.
g) Assume that p = 0 (such that utility per capita gets the same weight independent of the time period) and consider the second Ramsey term (a. g). If g is negative, future generations have (lower/higher) _consumption per capita and since a is positive, the term "a *g" will be (negative, positive) so the SDR will be _(negative, positive) which puts (more, less) weight on the early generations abatement costs relative to future generations benefits. The bigger is alpha (a), the (higher/lower) is the tolerance for intergenerational inequality which makes the term "a g" even more (negative, positive) and also the SDR is even more (negative, positive) putting even more weight on (current, future) generations' surplus changes. If g <0, early generations are (poorer, richer) in terms of per capita consumption, so it makes sense to put (more, less) weight on their abatement costs relative to future per capita damage reduction benefits due to the principle (diminishing, increasing, constant, decreasing) marginal utility.
h) One economist, Richard Tol assumes a utility discount rate of p = 0.03 in some model runs. Using this rho, find the present value of the 100 happiness units ("utils") experienced in 2050. Based on this, when you are 50 years old, your utility per capita would be counted as how many times higher than your utility per day? Find the present value of 100 happiness units in the year 2120. Would you recommend this high discount rate? Briefly explain.
i) The utility discount rate (p) determines weights on (utility per capita, real consumption units per capita) in different time periods while the SDR discounts determines the weights on (utility per capita, real consumption units per capita). j) Based on the concept of the vale of ignorance, if you had not yet been born and had equal chances of being born in the year 2020 or 2120, which analyst would you prefer was in charge of GHG abatement decisions made in the year 2020? Justify your answer.