Trade1 ECON 4925 Autumn 2010 Hydropower economics Lecture 13 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 The social planning problem with trade constraint
Trade 8 The Lagrangian function
Trade 9 The Kuhn – Tucker conditions
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
Trade 11 Trade between countries Hydro and Thermal The social planning problem in Thermal Unlimited trade to exogenous prices
Trade 12 The Lagrangian function Inserting the energy balance
Trade 13 The Kuhn – Tucker conditions The second equation holds with equality because the trade variable is unrestricted in sign
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
Trade and transmission 15 Trade between Hydro and Thermal The cooperative social planning problem
Trade and transmission 16 The Lagrangian function Inserting the energy balances Export for one country is import for the other
Trade and transmission 17 The Kuhn – Tucker conditions
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