ECON 4930 Autumn 2007 Electricity Economics Lecture 9

1. ECON 4930 Autumn 2007Electricity EconomicsLecture 9 Lecturer: Finn R. Førsund Market power

2. Background • The use of market power is a potential problem of the deregulated electricity sector • 20 % of the world’s electricity is produced by hydropower and 1/3 of the countries have more than 50% • Hydro power is a special case due to zero variable cost, water storage, high power capacity and maximal flexible adjustment Market power

3. Monopoly • Using the simplified model of total water availability based on reservoir constraint not binding • Maximising profit over the planning horizon Market power

4. Difference between objective functions for social planning and monopoly • Objective function social planning • Area under the demand function (zero variable costs) • Objective function monopoly • Producer surplus: total revenue (zero variable costs) Market power

5. Solving the monopoly optimisation problem • The Lagrangian • The Kuhn – Tucker conditions Market power

6. Interpretations of optimality conditions • Assuming positive production in all periods • Introducing demand-flexibility corrected prices • Demand flexibility (negative) • Demand flexibility (demand function on price form) is the inverse of demand elasticity (demand function on quantity form) Market power

7. Interpretations, cont. • Optimality condition: flexibility - corrected prices equal for all time periods • Market prices will vary with relative elastic periods having lower prices than relative inelastic periods Market power

8. Bathtub illustration of two periods Period 2 Period 1 p2M p1S= λS p2S =λS p1M λM Market power

9. Spilling and monopoly • Depending on the characteristics of the demand functions it may be optimal for the monopoly to spill water • Spilling can be regulated by prohibition • Introducing an equality constraint • Zero-spilling regulation will reduce the monopoly profit Market power

10. Spilling and zero-spilling regulation Period 2 Period 1 p1 p2 p2M p1M Total available energy Market power

11. Spilling and zero-spilling regulation Period 2 Period 1 p1 p2 p2M p1M λ<0 λ<0 Total available energy Market power

12. Limited reservoir and the social solution • Reservoir dynamics: water at the end of a period = water at the end of previous period plus inflow minus release of water during the period • Shadow prices on water and reservoir limit recursively related, solving using backward induction (Bellmann) • Overflow is waste • Social price may vary if reservoir constraint is binding Market power

13. Limited reservoir and monopoly • The flexibility-corrected price substitute for the social price • Flexibility-corrected prices may differ if reservoir constraint is binding • Social solution may be optimal if constraint is binding • Differences with social solution depend on the demand elasticities • Spilling may be optimal Market power

14. Monopoly with reservoir constraint Market power

15. Solving the monopoly optimisation problem • The Lagrangian function Market power

16. Solving, cont. • The Kuhn – Tucker conditions Market power

17. Interpretation of conditions • Assuming positive production in all periods • Using flexibility-corrected prices • Assuming positive flexibility-corrected prices is a stronger assumption than non-satiation • General shifting strategy still valid Market power

18. Illustration of monopoly solutionwith reservoir Period 2 Period 1 p2M p2S p1S p1M λM D A B C Market power

19. Illustration of monopoly solutionwith reservoir Period 2 Period 1 p2M p2S p1S p1M 2M 1 1M D A B C Market power

20. Illustration of monopoly solutionwith reservoir Period 2 Period 1 p2M p2S p1M p1S p1M p1S 2M 1 1M D A B C Spill Market power