Trade1 ECON 4925 Autumn 2007 Electricity Economics Lecture 6 Lecturer: Finn R. Førsund

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

Trade 3 Opening up for free trade The social planning problem New symbols

Trade 4 The Lagrangian Inserting the energy balance because it has to hold as an equality

Trade 5 The Kuhn – Tucker conditions  The second equation holds with equality because trade variable is unrestricted in sign

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

Trade 7 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

Trade 8 The social planning problem with trade constraint

Trade 9 The Lagrangian function

Trade 10 The Kuhn – Tucker conditions

Trade 11 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

Trade 12 Trade between countries Hydro and Thermal The social planning problem in Thermal  Unlimited trade to exogenous prices

Trade 13 The Lagrangian function Inserting the energy balance

Trade 14 The Kuhn – Tucker conditions  The second equation holds with equality because the trade variable is unrestricted in sign

Trade 15 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

Trade 16 Trade between Hydro and Thermal The cooperative social planning problem

Trade 17 The Lagrangian function Inserting the energy balances  Export for one country is import for the other

Trade 18 The Kuhn – Tucker conditions

Trade 19 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 = ImportExpor t Hydro Thermal A'A'A M'M' M B'B'B

Trade 20 p 1 Th =p 1 H = 1 Trade Hydro –Thermal with reservoir constraint Period 1 Period 2 c'c' c'c' Import θ2θ2 p 2 Th =p 2 H = 2 A B C D Import Export Hydro Thermal Export γ1γ1 A'A' D'D'