Endogenous Social Discount Rate, Sustainability: Do we have the Right to Discount Future Generations Utility?

Transcription

1 Endogenous Social Discount Rate, Right to Discount Institute of Social Science, University of Tokyo 21st June 2013

2 Why do we discount? Ethical Problem (Dasgupta 2008) This means that some transcendent value judgment should be necessary for permitting utility discounting. Koopmans (1960) and Diamond (1965) reveal that there are paths which contradict with their value judgments if we apply no-discounting. Cowen (1992) and Blackorby et al. (1995) also find that no-discounting is desirable if we admit their own value judgments.

3 The Outline of the Paper Based on a simple consumption/co 2 emission model, we solve the optimum social discount rate without introducing any transcendent value judgment. The methodology is as follows: first, we solve the optimal proportional carbon tax rate in a stationary market economy; second, we solve the planning problem which attains the same allocation as that in the market economy, and obtain the optimal social discount rate by Negishi (1960) method.

4 The Outline of the Paper(continued) The resultant solution reveals that the optimal discount rate is zero. We also show that the optimal emission-suppressing policy is time consistent in the sense that such a policy makes all generations better off.

5 The Outline of the Paper(continued) Although the model is solved within finite-time horizon, we can extend the solution to the infinite-time horizon case, and thereby succeeding in justifying the following social utility function used by Dutta (1991), Broom (1992), and Cline (1992): 1 lim T + T T u(c t, e t ). (1) t=0

6 The Outline of the Paper(continued) Since we can obtain the absorption rate of oceans to emitted CO 2 by Takahashi et at. (1980), although it is a round number, we can calculate the second-best proportional carbon tax rates θ and their corresponding social discount rate SDR as follows.

7 Table 1: The Social Discount Rate and the Second-Best Carbon Tax Rate SDR(1) SDR(20) θ (%) SDR(1): Social Discount Rates per anuum SDR(20): Social Discount Rates per 20 years θ: Carbon Tax Rates

8 Intuition on Why the Optimal Social Discount Rate is Zero Suppose that the applied gross social discount rate SDR < 1. This implies that current generation is preferred to future generations. Because CO 2 emission affects the decedents as a negative externality, also because such an aggravation in utilities is discounted if SDR < 1, the economy experiences the excess consumption/emission. If SDR > 1, every current generation is forced to self-sacrifice, thereby the economy falling into the shortage of consumption and excessively clean atmosphere. As such, the optimal SDR = 1

9 The Optimal Plan is Time Consistent Definition of Time Consistency: We call a plan is time consistent iff the plan maximizes not only current generation s utility but also each descending generation. The Optimal plan (zero discounting) is time consistent.

10 Heuristic Explanation on Why Time Consistency Holds There is the following one-to-one correspondence between the optimal SDR and the required sustainable utility level U. That is,. SDR = Λ(U) This conversely implies that once we give SDR in advance, the corresponding sustainable utility is uniquely determined as. U = Λ 1 (SDR)

11 Heuristic Explanation on Why Time Consistency Holds(continued) Since each generation attains the same utility level in a stationary state, the optimal SDR = 1, and every constraint is binding, max L = max U = max U = Λ 1 (0) holds. L is the Lagragean for the social planning under the constraint of sustainability. Thus, whenever we set SDR = 1 a priori, the obtained utility of each generation is maximized on U. In other words, the no-discounting social planning maximizes each generation s utility equally, and hence this plan is time consistent.

12 The Infinite Time Horizon Case Since no-discounting implies that the utility of each generation in the social welfare function should be equally weighted, we can choose the weight as 1 where T is the length of the planning. T When T +, we obtain the no-discounting and converging social welfare function SW as SW 1 lim T + T T u(c t, e t ). t=1