The Optimal Timing of Transition to New Environmental Technology in Economic Growth

1. The Optimal Timing of Transition to New Environmental Technology in Economic Growth 2009 International Energy Workshop 17-19 June, 2009 Fondazione Giorgio Cini, Venice Italy Akira MAEDAand Makiko NAGAYA Kyoto University

2. Background: Growth and the Environment • Natural resource use along w/ economic growth has been studied since 1970s. • Dasgpta and Heal (1974), Stiglitz (1974), Solow (1974), etc. • In 1980s, the environment began to be recognized as another important factor that determines the trajectories of growth. • At the same time, the theory of economic growth began to change. • “endogenous change” comes to a central issue in the economic literature, inc. Romer (1990)，Lucas (1988), etc. • These two streams converge to a bunch of studies after late 1990s. • Endogenous technological change plays central roles in sustainable development. • Barbier (1999), Tahvonen and Salo (2001), Bovenberg and Smulders (1995), Schou (2000), Groth and Shou (2002),Cunha-e-Sá and Reis (2007)

3. Background: Optimal Timing (1) • Cunha-e-Sá and Reis (2007). “The Optimal Timing of Adoption of a Green Technology.” Environmental andResource Economics 36. • Their focus: • As the economy grows, new pollution-abating technology becomes indispensable; • Such a technology requires investment efforts at the time of deployment; • The optimal timing will be determined in an endogenous manner. • Their model • is based on a typical Ramsey-type model, incorporating “environmental quality” and “clean technology.” • The level of clean technology may change discontinuously once “grade-up” happens. • Consideration for the net benefit determines the optimal timing of grade-up.

4. Background: Optimal Timing (2) • Cunha-e-Sá and Reis contributed to the literature in that: • they underlined the significance of “the optimal timing” in the framework of the environment and economic growth. • Some debatable issues remain on the other hand: • Technological change in clean technology is represented as a jump of the level. • Allowing such a sudden change of the level implies that the technology is a kind of flow, not stock. • This nature contrasts to the fundamental idea of modern endogenous growth theory: their treatment of technological change for clean technology thus seems old-fashioned in this respect. • Their treatment of investment-related costs seems strange. • It may degrade the clear cut of their analysis.

5. The Purpose • is to examine the choice of timing for technological change vis-à-vis environmental quality in economic development. • Based on the spirit and mathematical treatment of Cunha-e-Sá and Reis, we develop an analytical model that addresses the optimal timing of transition of environmental technology from old one to new one. • In contrast to Cunha-e-Sá and Reis, • we focus upon acceleration of technological progress, and • we treat costs in a simpler manner so that our focus can become clearer.

6. Analytical Frame (1) • Ramsey model w/ closed economy; constant population • Y: Production; K: Capital stock; C: Consumption • Q: Environmental quality • a: Environmental technology level • A representative economic agent represents the household whose time-additive utility is determined by not only consumption (C) but also “environmental quality” (Q).

7. Analytical Frame (2) • The environmental quality (Q) is a function of the consumption (C) and “environmental technology level” (a) • The progress of the environmental technology level itself may occur as the economy grows. • the growth rates of a and K ( Y/A)are proportional to each other: • That is: • The coefficient may change discontinuously at time T.

8. Analytical Frame (3) • Discontinuous change in the coefficient : • Costs for the change • Typical costs: R&D and physical investments • Existing physical capital may become obsolete, and need to be scrapped.

9. s. t. The Model

10. Solving the Problem Control variables: T, State variables: • First step: Optimizing for the value function to a given capital stock for after-transition. • Second step: Finding the optimal path until the transition. • Third step: Solving for the optimal timing.

11. s. t. tT First Step • Suppose that transition to the new technology occurred at time T. • The problem thereafter is: • FONCs:

12. (constant) where We obtain: Solution for the First Step

13. s. t. Second Step • Finding the optimal path to time T • FONCs:

14. where We obtain: Solution for the Second Step

15. where KT has already been obtained analytically. if if The Final Step • Optimizing it w.r.t. T • Thus, we obtain: • Examining its sign, we know the properties of the solution.

16. or, equivalently Proposition 1 For a finite T*to exist, that is, T*< , the following condition is necessary: Conversely, if holds, then the transition of environmental technology never occurs. (i.e. T*= )

17. Interpretation of Prop. 1 (1) • The existence of a finite transition time is determined by: • Notice: • represents the magnitude of the elasticity of marginal utility. • It determines the sign of the cross second derivative of the utility function: • If 1> (1<), marginal utility of “environmental quality” U/Qis increasing (decreasing) in consumption. • That is, the society prefers more (less) environmental quality as the consumption grows. This represents average consumption propensity just before the transition.

18. Interpretation of Prop. 1 (2) • For the transition to occur in a finite time horizon, the economy must be in either of the following two situations: • The economy highly prefers environmental quality, and its current average consumption propensity is lower than a certain value (1/). (The economy has a higher saving rate.) • The economy rather prefers consumption to environmental quality, and its current average consumption propensity is higher than a certain value (1/). (The economy has a lower saving rate.)

19. Proposition 2 Suppose that the following conditions hold. And, either and and or Then there exists an optimal transition time T* such that 0 < T*< , and it is obtained by solving the following equations:

20. Given the existence of a finite T*, case: Capital stock Kt increases, and reaches the fixed level from below. case: Capital stock Kt declines, and reaches the fixed level from above. Interpretation of Prop. 2

21. Suppose Also, suppose the following approximations hold. Then, we have following sensitivities. case: case: Note: Proposition 3

22. represents the degree of the innovation. Intuitively, it tells how much the transition to the new environmental technology is beneficial to the economy. The increase makes the barrier to transition lower. Interpretation of Prop. 3

23. Conclusion • We investigated the optimal timing of transition in environmental technology from old one to new one along with economic growth. • Whether transition to new technology is needed or not is determined by two factors: the degree of complementarity between environmental quality and consumption, and the average consumption propensity (or saving rate). • Given the necessity, transitions to new technology may occur in two possible ways. • An environmentally developing economy would accumulate social capital and invest it to the development of the new technology. • A matured economy holding a sufficiency of capital and enjoying a high consumption rate would realize the need for environmental quality improvement in some day. • A higher degree of innovation would lead to earlier or later transitions, respectively.