Market power1 ECON 4925 Autumn 2006 Resource Economics Market power 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 effect capacity and maximal flexible adjustment

Market power 3 Plan of the talk The basic hydropower model Hydropower model with limited reservoir Hydropower and thermal power Hydropower with thermal competitive fringe

Market power 4 The basic hydropower model Discrete time periods (weeks) over a natural inflow cycle (one year) Deterministic demand and total water All inflow occur in the first period, e.g. after snow melting, spring rain, autumn rain The reservoir limit of the system will not be reached Zero variable costs in the hydro system Only variable cost alternative value of water

Market power 5 Social utilisation of water Social planning: maximising sum of consumer plus producer surplus = area under the demand curves No discounting Free terminal value of reservoir Optimal solution: arbitrage price of stock of water (Hotelling); marginal willingness to pay (price) equal for all time periods

Market power 6 The monopoly model Problem formulation The Lagrangian First-order condition

Market power 7 The monopoly model, Interpretation of the conditions Maximising profit introduces marginal revenue functions Marginal revenue can be expressed as demand- flexibility corrected prices 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 Social optimum, and monopoly p 1 (e 1 H ) p2Mp2M Period 1 Period 2 p 2 S = λ S p 1 S = λ S p1Mp1M λMλM p 2 (e 2 H )

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 Zero-spilling regulation will reduce the monopoly profit

Market power 10 Spilling and zero-spilling regulation p1Mp1M Period 2 λ<0 Period 1 p2Mp2M λ<0 Total available energy p2p2 p1p1

Market power 11 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 12 Limited reservoir and monopoly Problem formulation The Lagrangian

Market power 13 Limited reservoir and monopoly, cont. First-order conditions

Market power 14 Limited reservoir and monopoly, cont. The flexibility-corrected price substitute for the social price Flexibility-corrected prices may differ if reservoir constraint binding Social solution may be optimal if binding constraint Differences with social solution depend on the demand elasticities Spilling may be optimal

Market power 15 Illustration of monopoly solution with r eservoir Period 1 p1Mp1M p2Mp2M A B C D Period 2 p1Sp1S P2SP2S λMλM p1Mp1M Spill λ2Mλ2M λ1Mλ1M

Market power 16 Hydro and thermal Thermal plants aggregated by merit order to a convex group marginal cost function Total capacity is limited Static problem: no start-up costs, no ramping constraints or minimum time on – off Shadow price on water equal to flexibility- corrected prices and equal to marginal cost of thermal capacity

Market power 17 Hydro and thermal, the model Problem formulation The Lagrangian

Market power 18 Hydro and thermal model, cont First-order conditions

Market power 19 Monopoly and extended bath-tub c’ λMλM Hydro energy p2Mp2M Period 1 Period 2 p1Mp1M Thermal extension a A B c C D d

Market power 20 Hydro with competitive fringe Thermal fringe modelled by a convex marginal cost function with limited capacity The fringe is a price taker and sets market price equal to marginal cost The dominant hydro firm must take fringe reaction into consideration Market power is reduced due to the fringe Conditional marginal revenue curve closer to demand curve due to market share less than 1 and fringe quantity adjustment

Market power 21 Hydro with competitive fringe; the model Problem formulation Fringe response Total differentiation

Market power 22 Hydro with competitive fringe First-order conditions

Market power 23 Hydro with competitive fringe, cont. Conditional marginal revenue Closer to the demand function due to  Market share effect  Fringe quantity reaction effect

Market power 24 The leader – follower game θ2θ2 p2p2 c’ p1p1 Thermal fringe λ λ A B C D E Hydro energy c’ Period 1Period 2

Market power 25 Extentions Hydro as competitive fringe  Hydro fringe can release all water just in one period, may restrict market power further Oligopoly game between hydro producers  Essentially a dynamic game, reduces the possibilities of strategic shifting of water  Quite complex to find solutions to dynamic gaming Uncertainty  Future water values become stochastic variables, system must avoid overflow or going dry, qualitatively the same problem for social planner and monopoly

Market power 26 Conclusions Hydro monopoly shifts water from relatively inelastic periods to elastic ones May be difficult to detect because variable cost is zero, only alternative value of water is variable cost and not readily observable Reservoir constraints, production constraints, etc. reduce the impact of market power Competitive fringe may block use of market power Fear of hydro market power exaggerated?