Water Exercise

BangkokUNDP-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

W

CS

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

0 100

W

33.3

10

32

Farmer 2

Farmer 1

Supply

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

0 100

W

33.3

10

32

Farmer 2

Farmer 1

Supply

70

CC

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?