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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 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 Demand for Water P W 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 CS for Water P CS W 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) Calculate Aggregate Value of Water • Calculate aggregate value of water to each farmer: – CS1=36W-0.2W^2 – CS2=50W-0.1 W^2 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 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 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? Allocation of Water P Farmer 2 33.3 Supply 32 Farmer 1 0 10 100 W 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 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 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 Allocation of Water P CC 33.3 Farmer 2 Supply 32 Farmer 1 0 10 70 100 W 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?