Jan Abrell Centre for Energy Policy and Economics (CEPE) D-MTEC, ETH Zurich. Renewable Resources I

Transcription

1 Renewable Resources I Jan Abrell Centre for Energy Policy and Economics (CEPE) D-MTEC, ETH Zurich Renewable Resources I

2 Outline So far Difference Equations Example: Fishery Example: Stock Pollution Summary Renewable Resources I

3 Classification of Resources Renewable Resources I

4 Hotelling Rule Socially efficient extraction Marginal utility of resource consumption raises with the discount rate Competitive extraction Prices rise with the interest rate Competitive industry achieves efficient extraction path Higher interest rate implies Sharper price increase Shorter time to exhaustion Renewable Resources I

5 Extensions: Extraction Cost and Monopoly Backstop technologies imply a choke-off price for natural resources Constant extraction cost (or taxes on resource extraction) below the chokeoff price lead to longer extraction horizon but resources will be fully used Monopolistic extraction leads to higher initial prices but more flat price path Longer extraction horizon Renewable Resources I

6 Today: What is a difference equation? a dynamic equilibrium and when is it stable? a net-growth and regeneration function? maximum sustainable yield? Renewable Resources I

7 Outline So far Difference Equations Example: Fishery Example: Stock Pollution Summary Renewable Resources I

8 Difference Equations Difference equation a recursive equation describes behavior of stock variable X in time G(X) describes the change of the stock as a function of the stock itself Renewable Resources I

9 Equilibrium Equilibrium Value of stock at which stock remains constant in time Equilibrium also called steady state, stationary state, fixed point, rest point Questions Existence of equilibrium? Stability of equilibrium? Renewable Resources I

10 How to find Equilibrium? Analytically Solve for roots of G(X) Graphically Plot G(X) and find roots Renewable Resources I

11 Stability of Equilibria An equilibrium is (asymptotically) stable if given a small exogenous shock the system again converges to the equilibrium point Check graphically Analytically: Stable if Renewable Resources I

12 Outline So far Difference Equations Example: Fishery Example: Stock Pollution Summary Renewable Resources I

13 Fishery Stock of fish in period t+1 depends on Stock of fish today: X t Net-growth function: F(X t ) Harvesting of fish: H t Net growth function determines growth of fish population depending on fish stock Expresses several aspects such as reproduction rate rivalry in nutrition quality of water Renewable Resources I

14 Logistic Net-Growth Function r > 0 K > 0 Intrinsic growth rate Environmental carrying capacity Small stock of fish Small stock, thus slow reproduction With increasing stock Reproduction rate increases But also rivalry in nutrition Renewable Resources I

15 Logistic Net-Growth Function: Natural Equilibrium Natural equilibrium Equilibrium without harvesting Solve for equilibrium Equilibria Renewable Resources I

16 Bio-Economic Equilibrium (with Harvesting) Solve for equilibrium Again two equilibria, of which one is unstable Renewable Resources I

17 Maximum Sustainable Yield Maximum sustainable yield (MSY) Maximum amount that can be harvested without extinction of the species Stock that support MSY Maximum harvesting Renewable Resources I

18 Outline So far Difference Equations Example: Fishery Example: Stock Pollution Summary Renewable Resources I

19 Stock Pollutant: CO 2 Environmental Targets

20 Stock Pollutants: Difference Equation Emissions increase pollution stock Regeneration function decrease of pollution stock Pollution stock Renewable Resources I

21 Outline So far Difference Equations Example: Fishery Example: Stock Pollution Summary Renewable Resources I

22 Difference Equations Difference equation a recursive equation describing behavior of stock variable X in time Solving for equilibrium An equilibrium is (asymptotically) stable if given a small exogenous the system again converges to the equilibrium point Renewable Resources I

23 Renewable Resources Logistic growth function depends on Intrinsic growth rate (r > 0) Environmental carrying capacity (K > 0) Two natural equilibria, one unstable Bio-economic equilibria with harvesting Maximum sustainable yield (MSY) Maximum amount that can be harvested without extinction of the species Renewable Resources I

24 Stock Pollutants Modeled as negative resources Concept of equilibria and stability remain the same Renewable Resources I

25 Literature Conrad, J. (2008): Resource economics. 2 nd edition. Cambridge University Press. Chapter 1, 3. Fees, E. and A. Seeliger (2013): Umweltökonomie and Umweltpolitik. 4 th edition. Vahlen. Chapter 13. Perman R., Y. Ma, J. McGilvray, and M. Common (2003): Natural Resource and Environmental Economics. Chapter 17. Renewable Resources I

26 Questions? Renewable Resources I