1. Water1 ECON 4925 Autumn 2006 Resource Economics Water as a natural resource Lecturer: Finn R. Førsund

2. Water 2 Economic use of water Rivers, lakes, groundwater Fish, transport, drinking water households, process water industry, irrigation agriculture, hydropower Hydropower: converting energy in falling water to electricity  Run of the river  Reservoirs

3. Water 3 The basic hydropower model Hydropower plants aggregated to one system Reservoir, stock of water R Inflows w and releases r The dynamics of water accumulation: R t  R t-1 + w t – r t, t=1,..,T  Inequality implies overflow Converting water from the dam to electricity e H t = (1/a)r t Fabrication coefficient a assumed to be constant

4. Water 4 The basic hydropower model, cont. Assuming a dominating period of inflows: all inflows come in period 1: Converting water to units of kWh: Assuming that the reservoir will never be full Perfect transferability of water between periods up to the horizon T (start of new cycle)

5. Water 5 Social evaluation of electricity Evaluation of electricity by utility functions Measuring utility in money Marginal willingness to pay and the demand function on price form

6. Water 6 The social planning problem Social planner’s optimisation problem The Lagrangian

7. Water 7 The solution Necessary first-order conditions Shadow price on water is zero if not all water is used Marginal willingness to pay, i.e. social price, equal for all periods

8. Water 8 The two-period bathtub illustration Total available electricity U 2 ’ = λ = p 2 U 2 ’(e 2 H ) e1He1H U 1 ’ = λ = p 1 Period 2 U 1 ’(e 1 H ) U1’U1’U2’U2’ Period 1 e2He2H

9. Water 9 Introducing discounting Discount factor: The optimisation problem Necessary first–order conditions

10. Water 10 The Hotelling rule Growth rate in marginal utility

11. Water 11 U 1 ’(e 1 H )β 1 The effect of discounting U 2 ’(e 2 H )β 2 U 2 ’β 2 = λ U 2 ’(e 2 H ) e1He1H U 1 ’β 1 = λ = p 1 Period 2 U1’U1’U2’U2’ Period 1 p2p2 Total available electricity e2He2H

12. Water 12 U 1 ’(e 1 H )β 1 The effect of increased discount rate U 2 ’(e 2 H )β 2 U 2 ’β 2 = λ U 2 ’(e 2 H ) e1He1H U 1 ’β 1 = λ = p 1 Period 2 U1’U1’ U2’U2’ Period 1 p2p2 Total available energy e2He2H

13. Water 13 The effect of more water U 2 ’(e 2 H )β 2 U 2 ’β 2 = λ U 2 ’(e 2 H ) U 1 ’β 1 = λ = p 1 Period 2 U 1 ’(e 1 H )β 1 U1’U1’ U2’U2’ Period 1 p2p2 Total available electricity e1He1H e2He2H