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ECON 4925 Autumn 2007 Electricity Economics Lecture 10 Lecturer: Finn R. Førsund Market power 1 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 Hydro power plants aggregated to a single plant Market power 2 Monopoly problem with hydo and thermal plants T max Th [( p ( x ) x c ( e t t t t )] t 1 subject to xt etH etTh T H e t W t 1 etTh e Th xt , etH , etTh 0, t 1,.., T T ,W , e Th given Market power 3 Solving the optimisation problem The Lagrangian function (eliminating total consumption) T L [ pt (etH etTh )(etH etTh ) c(etTh )] t 1 T t (etTh e Th ) t 1 T ( etH W ) t 1 Market power 4 Solving the optimisation problem, cont. The Kuhn – Tucker conditions L H Th H Th H Th p ( e e )( e e ) p ( e e t t t t t t t t ) 0 H et ( 0 for etH 0) L H Th H Th H Th Th p ( e e )( e e ) p ( e e ) c '( e t t t t t t t t t ) t 0 Th et ( 0 for etTh 0) T 0 ( 0 for etH W ) t 1 t 0 ( 0 for etTh e Th ) Market power 5 Interpreting the optimality conditions Assumption: both hydro and thermal capacity is used pt ( xt )(1 t ) c(etTh ) t Flexibility-corrected price equal to water value equal to marginal thermal costs (plus shadow value on the capacity constraint) Same amount of thermal capacity used in each period Market power 6 Monopoly and extended bath-tub Period 1 Period 2 p2M p1M λM c’ c’ a A B c C D d Hydro energy Thermal extension Market power 7 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 8 The optimisation problem of the dominant hydro firm T max H p ( x ) e t t t t 1 subject to xt etH etTh T H e t W t 1 pt ( xt ) c(etTh ) xt , etH , etTh 0, t 1,.., T T ,W given Market power 9 The reaction of the competitive fringe Finding the reaction of the fringe to the quantity of the dominant firm pt (etH etTh ) c(etTh ), t 1,..,T Solving for thermal output as a function of hydro output etTh ft (etH ), ft 0 (t 1,.., T ) Market power 10 The reaction of the competitive fringe, cont Determining the sign of the reaction function Differentiating the behavioural condition pt (etH etTh )(detH detTh ) c(etTh )detTh detTh pt (etH etTh ) 0 (t 1,.., T ) H H Th Th det pt (et et ) c(et ) Market power 11 Solving the optimisation problem of the dominant hydro firm The Lagrangian function T L pt (etH ft (etH ))etH t 1 T ( etH W ) t 1 The Kuhn – Tucker conditions Th de L H Th H Th H t p ( e e ) p ( e e ) e (1 ) 0 t t t t t t t H H et det ( 0 for etH 0) T 0 ( 0 for etH W ) , t 1,.., T t 1 Market power 12 Interpretations Signing of the expression (1 + detTh/detH) detTh pt (etH etTh ) 1 H 1 H Th Th det pt (et et ) c(et ) c(etTh ) 0 H Th Th pt (et et ) c(et ) Market power 13 Interpretations, cont. Decomposition of conditional marginal revenue MRt pt c etH detTh H pt (1 t H ) pt H et , t 1,.., T Th et et det Conditional marginal revenue curve closer to demand curve due to Market share less than 1 Fringe reaction of increasing output when price increases Market power 14 A constraint on fringe thermal capacity Advantage for the dominant firm when fringe capacity constraint is biting Limit on the fringe quantity reaction pt ( xt ) ct(etTh ) t t 0 ( 0 for e e ) Th t Th Fringe response etTh e Th for pt ( xt ) p c(e Th ) Market power 15 The leader – follower game Period 1 Period 2 p2 θ2 c’ p1 c’ λ λ A B C D E Hydro energy Thermal fringe Market power 16 Extentions Hydro as competitive fringe Oligopoly game between hydro producers Hydro fringe can release all water just in one period, may restrict market power further 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 17 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? Market power 18