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Water Exercise

Water Exercise. Bangkok UNDP-ADAPT ASIA. 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.

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Water Exercise

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  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 CS W

  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 Farmer 2 33.3 Supply 32 Farmer 1 0 10 100 W

  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 CC Farmer 2 33.3 Supply 32 Farmer 1 70 0 10 100 W

  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?

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