ECON 4910 Spring 2007 Environmental Economics Lecture 2 Chapter 6

1. ECON 4910 Spring 2007 Environmental Economics Lecture 2 Chapter 6 Lecturer: Finn R. Førsund Environmental Economics

2. The Coase theorem • Provided some assumptions are fulfilled, the initial property right to an environmental resource does not matter for the social efficiency of the utilisation of the resource • Maximising profit or utility bargaining between the parties will lead to the same use of the environmental resource independent of the alocation of property rights Environmental Economics

3. Consider the basic model • Benefit function is associated with a steel mill emitting pollutants • Damage function is associated with a downwind laundry drying clothes outdoors Environmental Economics

4. Behind the benefit function we have the multiple output production function • Pollution without regulation • pollution corresponding to private profit maximisation • Pπ = g(x*) Environmental Economics

5. Interpretation of the benefit function • The benefit function reflects the costs of reducing the amount of pollution, P, generated in steel production, i.e. by purification and/or output reduction, from a level equal to the private profit maximisation level Pπ to a lower level • Notice that it is also costly for the steel mill to increase the level of pollution beyond Pπ. The b’(.) – function has a discontinuity Environmental Economics

6. Allocating property right to clean air • The steel mill has the right to pollute • The laundry has the right to clean air • Pmin is found by solving d’(P) = 0 d’(P) b’(P) P P* PMin Pπ Environmental Economics

7. Asumptions for the Coase theorem • No transaction costs • Perfect information • Agents price-takers • Maximize profit (utility) • Costless enforcement of agreements • No income and wealth effects Environmental Economics

8. Elements of general equilibrium models of the environment • Basic stages: • (1) Extracting/harvesting resources • (2) Transformation of resources into products • Residuals as by-products (Primary/secondary residuals if add-on purification is an option) • (3) Environmental impacts of absorption of residuals • (4) Evaluation of changes in environmental indicators • Evaluation through utility functions, environment as public good, or damage functions. • Products are also evaluated either through utility functions or benefit functions Environmental Economics

9. Strands of models according to level of aggregation • Aggregated macro level: • General equilibrium and interdependencies most important, skip details about resource creation, production structure, general abatement possibilities. • Micro level of the firm: • Detailed production function and purification possibilities, household production functions • Classical externalities models: • Short- circuits the environment, direct representation of residual-generating activities in production and/or utility functions Environmental Economics

10. Why general equilibrium models • Overview of complexities, interdependencies in the economy and economic - environmental interactions, expose weaknesses of partial analyses • Establish concepts or variables fruitful for empirical work. • Show the type and extension of information needed to implement any optimal solution • Show possibilities for decentralised decision-making • Framework for study of distributional aspects of pollution and pollution abatement Environmental Economics

11. An aggregated general equilibrium model • Model without resource extraction and inputs • Multiple outputs that generate pollutants • Environmental services influences by pollutants • Environment as a public good Environmental Economics

12. Formulating the social optimisation problem Environmental Economics

13. Solving the model • Simplifying the model by eliminating variables • The Lagrangian function Environmental Economics

14. Differentiating wrt all endogenous variables • Endogenous variables yi,xij,M • Necessary first –order conditions Environmental Economics

15. Interpreting shadow prices • The marginal effect in the optimal solution of changing constraints • μi : shadow price on the distribution constraint, if the shadow price is zero, then giving more of it to a person has no opportunity cost • γ: shadow price on the transformation function, if the shadow price is zero, then there is no cost of production • λ: shadow price on the environmental service function, if the shadow price is zero, then there is no environmental cost of pollution Environmental Economics

16. Interpreting inequalities • If the first-order conditions hold with inequalities then the endogenous variable in question should be set to zero • The supply of good i condition • inequality means that the production and pollution cost is higher than the shadow price  the good should not be supplied • The allocation condition of a good to an individual • inequality means that the weighted social value of the good is lower than the shadow price  the good should not be supplied to the individual Environmental Economics

17. Interpreting inequalities, cont. • The environmental service condition • inequality means that the weighted social value of the environmental good summed over all individuals is lower than the shadow price of the environmental good the environmental good should not be supplied Environmental Economics

18. Standard procedure of solution • Assume interior solutions, i.e. all first-order conditions hold with equality (back to standard Lagrange with equality constraints) • Eliminating two of three Lagrangian parameters • Marginal costs equal to marginal benefits Environmental Economics

19. Forming MRT and MRS Environmental Economics

20. Implementing the solution via competitive markets • Profit maximisation to prices pi • Necessary first-order conditions • MRT assuming interior solutions Environmental Economics

21. Implementing the solution, cont. • Consumers maximising utility given income, Ri • Necessary first-order conditions Environmental Economics

22. Implementing the solution, cont. 2 • MRT = MRS • A competitive market system will not realise a Pareto optimum. The environmental costs are left out of the market system. M is a public good, no producer is providing this good and selling it to consumers Environmental Economics