ECON 4925 Autumn 2010 Hydropower economics Lecture 13

ECON 4925 Autumn 2010 Hydropower economics Lecture 13 Lecturer: Finn R. Førsund Trade 1

Unconstrained trade n n n 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 2

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

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

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

Trade and the bathtub diagram for two periods p 1 Period 2 p 2 XI = 2 p 1 AU γ 1 p 2 AU p 1 XI = 1 Import A x 1 A' B AAU B' C C' x 2 D Total available water Trade 6

The social planning problem with trade constraint Trade 7

The Lagrangian function Trade 8

The Kuhn – Tucker conditions Trade 9

The bathtub diagram for two periods p 1 Period 2 Period 1 p 2 XI α 2 p 2= 2 γ 1 p 1= 1 p 2 p. AU β 1 p 1 XI Import x 1 A Prod. 1 Export Cons. 2 B C x 2 D Total available water Trade 10

Trade between countries Hydro and Thermal n The social planning problem in Thermal q Unlimited trade to exogenous prices Trade 11

The Lagrangian function n Inserting the energy balance Trade 12

The Kuhn – Tucker conditions q The second equation holds with equality because the trade variable is unrestricted in sign Trade 13

Illustrating two periods Period 1 Period 2 p 2 XI=p 2 θ 2 c' p 2 AU p 1 AU c' p 1 XI=p 1 Import c' (0) Export x 2 x 1 A x 1 B O Trade C D 14

Trade between Hydro and n The cooperative social planning problem Thermal Trade and transmission 15

The Lagrangian function n Inserting the energy balances q Export for one country is import for the other Trade and transmission 16

The Kuhn – Tucker conditions Trade and transmission 17

Combining the bathtub diagram and thermal diagram for two periods Period 2 Period 1 θ 2 p 1 Th=p 1 H= p 2 Th=p 2 H= c' c' Export Import A' Export Thermal A M' M B' Hydro Trade and transmission B Import Thermal 18