1. Water Exercise Bangkok UNDP-ADAPT ASIA

2. Estimating Irrigation Demand Agricultural study will collect data on net revenue and water use for irrigated farms Regress net revenue (NR) on water (W) and other control variables (X) NR=a0+a1W+a2W^2+BX Coefficients ai estimated by regression

3. Calculate Marginal Value Water Differentiate NR equation with respect to W dNR/dW=a1+2a2W Expectation is that a1>0 and a2<0 dNR/dW is the net (of fee) marginal value of water to farmer If there is a fee F for water, the marginal value of water P=dNR/dW+F P is expected to decline as farmers get more water

4. Demand for Water P W

5. Value of Water Marginal value of water: – P= a1+a2W+F (with a2<0) Aggregate value (CS) of water is sum of marginal values from 0 to W It is the area underneath the demand function – CS=∫P dW – CS=a1W+(a2/2)W^2+FW

6. CS for Water P W CS

7. Allocating Water Suppose two farmers want to use the water in a watershed Supply of water is 100 and no fees Inverse demand by farmer 1 is: – P=36-0.4W1 Inverse demand by farmer 2 is: – P=50-0.2(W2)

8. Calculate Aggregate Value of Water Calculate aggregate value of water to each farmer: – CS1=36W-0.2W^2 – CS2=50W-0.1 W^2

9. Evaluate Farmer 1 Values Enter values for Farmer 1 water from 1 to 100 – Enter “1” in location A2 – Enter “=a1+1” in location A3 – Copy and paste formula in locations A4 to A101 Calculate CS of farmer 1 in location B2 – Enter “=36*a1- 0.2*(a2^2)” – Copy and paste formula in B3 to B101

10. Evaluate Farmer 2 Values Enter values for Farmer 1 water from 1 to 100 – Enter “=100-A2” in location C2 – Copy and paste formula in locations C3 to C101 Calculate CS of farmer 2 in location D2 – Enter “=50*C2- 0.1*(C2^2)” – Copy and paste formula in D3 to D101

11. Calculate Aggregate Value In Column E, sum values Enter in location E2 “=B2+D2 Copy and paste formula in E3 to E101 What allocation maximizes value of water?

12. Allocation of Water P 0100 W 33.3 10 32 Farmer 2 Farmer 1 Supply

13. Optimum Allocation Optimum maximizes sum of values across all users Equates marginal value of every user Equate P of farmer 1 to P of farmer 2 P=36-0.4W=50-0.2(100-W) W1=10 W2=100-10=90 P=32

14. Climate Change Suppose climate change reduces supply of water from 100 to 70 (30% loss) What is new optimal allocation? Enter into location F2 “=70-A2” Copy and paste into F3 to F76 Enter into location G2 “=50*F2-0.2*(F2^2) Sum columns C and G into H2 to H76

15. New Allocation Optimum allocation equates P given new supply P=36-0.4W=50-0.2(70-W) W=0 W2=75 P=36 Not same percentage reduction across both farmers

16. Allocation of Water P 0100 W 33.3 10 32 Farmer 2 Farmer 1 Supply 70 CC

17. Suboptimal Allocation Make both users have 30% reduction Farmer 1 goes from 10 to 7 Farmer 2 goes from 90 to 63 What is total value of this outcome?