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Trade1 ECON 4925 Autumn 2010 Hydropower economics Lecture 13 Lecturer: Finn R. Førsund
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Trade 2 Unconstrained trade Consider two countries (regions) linked by an interconnector, home country and abroad Loss on the interconnector is disregarded Trade during a period is the net flow, i.e., either import or export The price of electricity abroad is exogenous Money is a new good in our partial model Trade income (expenditure) is just added (subtracted from) to the social value of electricity consumption
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Trade 3 Opening up for free trade The social planning problem New symbols
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Trade 4 The Lagrangian Inserting the energy balance because it has to hold as an equality
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Trade 5 The Kuhn – Tucker conditions The second equation holds with equality because trade variable is unrestricted in sign
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Trade 6 Trade and the bathtub diagram for two periods γ1γ1 p1p1 Period 2Period 1 Total available water p2p2 Import A x1x1 A' B A AU B' CC' x2x2 D p 1 AU p 2 AU p 2 XI = 2 p 1 XI = 1
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Trade 7 The social planning problem with trade constraint
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Trade 8 The Lagrangian function
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Trade 9 The Kuhn – Tucker conditions
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Trade 10 The bathtub diagram for two periods p1p1 Prod.1Cons.2 Import Export Total available water p2p2 α2α2 β1β1 γ1γ1 p AU Period 1 Period 2 x1x1 A BCD x2x2 p 1 = 1 p 1 XI p 2 XI p 2 = 2
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Trade 11 Trade between countries Hydro and Thermal The social planning problem in Thermal Unlimited trade to exogenous prices
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Trade 12 The Lagrangian function Inserting the energy balance
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Trade 13 The Kuhn – Tucker conditions The second equation holds with equality because the trade variable is unrestricted in sign
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Trade 14 Illustrating two periods Period 2Period 1 ExportImport c'c' c'c' θ2θ2 c' (0) x2x2 x1x1 x1x1 A B C OD p 1 AU p 1 XI =p 1 p 2 AU p 2 XI =p 2
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Trade and transmission 15 Trade between Hydro and Thermal The cooperative social planning problem
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Trade and transmission 16 The Lagrangian function Inserting the energy balances Export for one country is import for the other
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Trade and transmission 17 The Kuhn – Tucker conditions
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Trade and transmission 18 Combining the bathtub diagram and the thermal diagram for two periods θ2θ2 Period 1 Period 2 c'c' c'c' Import Export p 1 Th =p 1 H = p 2 Th =p 2 H = ImportExport Hydro Thermal A'A'A M'M' M B'B'B
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