1. An application of the logistic curve to the modeling of CO 2 emission reduction Kazushi Hatase Graduate School of Economics, Kobe University

2. 2007/5/24Rokko Forum, Kobe University2 The model and simulations of this study  Global economy is viewed as a two-sector Ramsey model  Energy sector of the model consists of two technologies:  Fossil fuel  New carbon-free technology  Diffusion of new technology is modeled by a logistic curve and learning-by-doing Model: RAMLOG Simulations  Varying the potential speed of technological change and the learning rate  Investigating the implication of the above two factors on the optimal CO 2 emission reduction pathways, cost of emission reduction and carbon tax levels

3. 2007/5/24Rokko Forum, Kobe University3 Model of global economy (the Ramsey model) 1.Intertemporal utility maximization 2.Production function L t ： labor inputs r t : pure time preference; r t = r 0 exp(-d r t) 3.Capital accumulation 4.Income accounts identity A t ： total factor productivity E t ： energy inputs p t : energy price

4. 2007/5/24Rokko Forum, Kobe University4 Logistic curve  Share of the new technology grows following a logistic curve  The equation above is modified into the following inequality form: S t ： share of new technology ： coefficient  We use a finite difference form in the computer program:

5. 2007/5/24Rokko Forum, Kobe University5 Logistic curve (continued)  Coefficient determines the speed of diffusion in the standard logistic function  It determines the “potential” speed of diffusion in the inequality form  In the inequality form, diffusion trajectory can take any paths under the logistic curve

6. 2007/5/24Rokko Forum, Kobe University6 Learning-by-doing  Assuming that the cost of new energy declines as experience increases W t ： cumulative experience b ： experience index TechnologyPeriodValue of b Nuclear (OECD)1975 – 19930.09 GTCC （ OECD ） 1984 – 19940.60 Wind (OECD)1981 – 19950.27 Photovoltaics (OECD)1968 – 19980.32 Ethanol (Brazil)1979 – 19950.32  Data of experience index （ source: McDonald & Schrattenholzer, 2001 ）

7. 2007/5/24Rokko Forum, Kobe University7 Learning-by-doing in the computer program  Using a finite difference form (Anderson & Winne, 2004)  Substituting W t by the cumulative installed capacity of new technology ： plant’s depreciation rate of new technology  Estimation of W 0 (Gerlagh and van der Zwaan, 2004) ： growth rate of new energy

8. 2007/5/24Rokko Forum, Kobe University8 Combining the Ramsey model, logistic curve and learning-by-doing Ramsey model Logistic curve Learning by doing

9. 2007/5/24Rokko Forum, Kobe University9 Climate change model  Adopt a simple CO 2 accumulation model (Grubb et al., 1995)  Anthropogenic CO 2 emission  Natural CO 2 emission （ Nordhaus, 1999 ）

10. 2007/5/24Rokko Forum, Kobe University10 Simulation scenarios  Simulation is lead to a time path of emissions that satisfies the stabilization target of 550 ppm (cost-effectiveness simulation)  Investigating how  Potential speed of technological change (coefficient a)  Leaning rate (experience index:b) affect the optimal CO 2 emission reduction Run: coefficient of logistic curveb: experience index STC + LL0.050.1 STC + HL0.050.5 FTC + LL0.20.1 FTC + HL0.20.5 STC: Slow Technological Change FTC: Fast Technological Change LL: Low Learning HL: High Learning  Model runs and parameter settings

11. 2007/5/24Rokko Forum, Kobe University11 Common parameters 1.For the parameters of the Ramsey model, RICE-99 (Nordhaus, 1999) and MERGE (Manne et al., 1995) are referred. 2.Energy inputs are measured in the equivalence of giga-tons of carbon (GtC) following RICE-99 (Nordhaus, 1999). 3.For the parameters of energy costs, Anderson and Winne (2004) is referred. 4.CO 2 accumulation model is calibrated by using the simulation results of a large-scale global climate model (Taylor et al., 1995) TechnologyInitial costLowest costInitial share Existing technology (O)3 c/kWh （ 3 c/kWh) 95.9% New technology (N)10 c/kWh3 c/kWh4%  Cost parameters

12. 2007/5/24Rokko Forum, Kobe University12 Calibration of the production function  Production function at t=0  Differentiating both sides and rearranging as follows:  A 0 is obtained by:

13. 2007/5/24Rokko Forum, Kobe University13 Optimal CO 2 emission pathways  Four emission pathways are not very different.  Learning-by-doing has almost no effect in STC (Slow Technology Change).

14. 2007/5/24Rokko Forum, Kobe University14 WRE emissions paths  Obtained by Wigley, Richels and Edmonds (Wigley et al., 1996).  Support deferring CO 2 emission reduction.

15. 2007/5/24Rokko Forum, Kobe University15 Optimal CO 2 reduction pathways  FTC + HL is a little similar to the WRE emissions paths.  The other three paths (either Slow TC or Low L) are flatter.

16. 2007/5/24Rokko Forum, Kobe University16 Optimal technology switch timing  Four pathways diverge much more than those of optimal CO 2 reduction.  Larger learning rate makes the starting point of diffusion earlier.

17. 2007/5/24Rokko Forum, Kobe University17 Emission reduction by energy input reduction and by new energy 1. STC + LL 2. STC + HL 3. FTC + LL 4. FTC + HL

18. 2007/5/24Rokko Forum, Kobe University18 Cost reduction of new energy  Cost reduction largely depends on the learning rate.

19. 2007/5/24Rokko Forum, Kobe University19 Loss of GWP through CO 2 emission reduction  GWP loss largely depends on the learning rate.  The larger the coefficient, the smaller is GWP loss (but, minor influence).

20. 2007/5/24Rokko Forum, Kobe University20 Carbon tax levels  Slow technological change or large learning rate leads to a larger carbon tax.  Carbon tax levels with the same learning rate are nearly the same up to the mid 21 st century.

21. 2007/5/24Rokko Forum, Kobe University21 Discussions 1.Some studies claim that the influence of learning-by-doing on the optimal CO 2 reduction is negligible. But, this study shows that learning-by-doing can affect emission reduction paths. Moreover, learning-by-doing has a significant influence on technology switch timing. 2.The optimal CO 2 reduction paths are relatively similar between the 4 model runs, while the optimal technology diffusion paths diverge. This can be explained by the proportion of the emission reduction done by energy input reduction and technology switch. 3.In the early period, emission reduction is mostly done by energy input reduction. 4.The results suggest that learning-by-doing creases positive externalities of innovation, reducing emission reduction costs and carbon tax levels.

22. 2007/5/24Rokko Forum, Kobe University22 Points to improve the paper 1.Making the parameters less dependent on Nordhaus’ RICE-99. 2.Considering the increase of fossil fuel costs. 3.GWP loss and carbon tax levels are high compared to some other studies. 4.Comparison of WRE emissions paths and the emissions paths of this study is not convincing enough. 5.Adding the figure of “CO 2 reduction by energy input reduction and by new energy”. 6.Rewriting the explanation about optimal CO 2 reduction paths and optimal technology switch timing. 7.Figure 4 “cost reduction of new energy” may not be necessary.