Market power1 ECON 4930 Autumn 2007 Electricity Economics Lecture 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 p2Mp2M Period 1 Period 2 p 2 S = λ S p 1 S = λ S p1Mp1M λMλM

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 p1Mp1M Period 2 Period 1 p2Mp2M Total available energy p2p2 p1p1

Market power 11 Spilling and zero-spilling regulation p1Mp1M Period 2 λ<0 Period 1 p2Mp2M λ<0 Total available energy p2p2 p1p1

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 solution with r eservoir Period 1 p1Mp1M p2Mp2M A B C D Period 2 p1Sp1S p2Sp2S λMλM

Market power 19 Illustration of monopoly solution with r eservoir Period 1 p1Mp1M p2Mp2M A B C D Period 2 p1Sp1S p2Sp2S 2 M 1 M 11

Market power 20 Illustration of monopoly solution with r eservoir Period 1 p1Mp1M p2Mp2M A B C D Period 2 p1Sp1S p2Sp2S p1Mp1M Spill 2 M 1 M 11 p1Sp1S