11th Annual Meeting of the International Water Resource Economics Consortium
The impact of Irrigation Capital
Subsidies on Common-pool
Groundwater Use and Depletion
Results for Western Kansas
Nicolas E. Quintana Ashwell
Graduate Research Assistant, Ph.D. Candidate
Jeffrey M. Peterson
Professor
Department of Agricultural Economics, Kansas State University
Background
•
More efficient technologies may result in higher water use and
faster aquifer depletion in certain river basins
•
•
Sheierling et al., 2006; Ward and Pulido Velazquez, 2008
“….optimal control would not enhance the welfare of farmers
compared with a strategy of free markets.”
•
•
Gisser and Sanchez, 1980
Without intervention, efficient irrigation technology adoption
may be slower than socially optimal.
•
Shah et al., 1995
Research Goal
Assess the effects of irrigation capital subsidies in a dynamic
common pool context.
•
Water extraction
•
Discounted welfare
and answer the questions
Can an irrigation capital subsidy policy capture
potential surplus?
How much?
Assumptions
Framework from Burness and Brill (2001) –
extension of Gisser and Sanchez (1980).
• Single-cell, unconfined aquifer
• Water is weakly essential input
• Water requirements set to meet FWY
Model
• Hydrology
•
Evolution of the water table height (elevation, ft) over time
H
•
1
 N  1   (k )  w
As
 '(k )  0
Declining yields from groundwater storage (AF/hr)
d

Y  2Q0 d  H (t )  Hc  
2

•
Water accounting identity/application efficiency
e(k )w  CR A
e(k )   0,1
de
(k )  0
dk
d 2e
(k )  0
dk 2
Model
• Costs:
Marginal cost of water
Marginal pumping costs ($/AF)
C  H t   
 SL  H t 
 H  t   Hc 
120
100
MC in $/AF
•
Cˆ (w, k ; H )  C ( H )w  (r   )kA  L(k )
80
60
40
20
0
•
Capital costs ($): (r   )kA
•
Labor cost associated to irrigation capital ($)
100
110
120
130
140
150
Lift (ft)
L(k )     wage
 : labor required for flood irrigation operation (hrs)
dL
(k )  0
dk
160
Model
•
Revenues($): revenue is area
under the Value Marginal Product
of Water (VMP).
Net Present Value of Net Farm
Benefits
t*
V  e
0
•
 rt
VMP of Water
250
200
VMPW($)
•
150
100
50
0
0
 R(e(k ) w)  Cˆ ( w, k ; H )  dt


20000
40000
60000
80000
100000 120000
Pumped water(AF)
VMP(40%)
VMP(80%)
Myopic solution:
Max R(e(k ) w)  Cˆ ( w, k ; H )
w, k
•
Planning solution: optimal control problem where w and k
are the control variables and H is the state variable.
Case Study: Sheridan Co, KS
Case Study: Sheridan Co, KS
Case Study: Sheridan Co, KS
Baseline Simulated Results
Simulation Results: Efficiency
0.8
110
0.75
100
Application efficiency
Water extraction ('000 acre-feet)
Simulation Results:
Water Extraction(AF)
90
80
70
60
50
0.7
0.65
0.6
0.55
40
30
0.5
0
50
100
150
200
0
50
100
Year
Myopic
150
Year
Planning
Myopic
Planning
200
Case Study: Sheridan Co, KS
Baseline Simulated Results
Simulation Results: Net Private
Benefits ($)
2645
7000
2640
Net PrivateBenefits ($ '000)
Water table elevation (ft above sea level)
Simulation Results: Water table
height(ft)
2635
2630
2625
2620
2615
2610
6000
5000
4000
3000
2000
1000
2605
0
50
100
150
200
0
50
100
Year
Year
Myopic
150
Planning
Myopic
Planning
200
Case Study: Sheridan Co, KS
Optimization given irrigation capital subsidy
Case Study: Sheridan Co, KS
Optimization given irrigation capital subsidy
Case Study: Sheridan Co, KS
Optimization given irrigation capital subsidy
Case Study: Sheridan Co, KS
Optimization given irrigation capital subsidy
Case Study: Sheridan Co, KS
Optimization given irrigation capital subsidy
Myopic
Planning
Subsidy
133.1
142.5
138
9.4
6.1
7.04%
3.64%
142.5
135.3
9.4
2.2
7.04%
1.67%
Net Farmer Benefits
NPV ($ millions)
Gain ($ millions)
Net Social Benefits
NPV ($ millions)
Gain ($ millions)
133.1
Case Study: Sheridan Co, KS
Conclusions
• Gains from management are larger than in
early studies
• Competitive capital underinvestment in the
short run but overinvestment in long-run
• Irrigation capital subsidies result in water
savings and small social welfare improvements,
capturing nearly 24% of potential surplus.
Q&A
This material is based upon work supported, in part, by the National Science
Foundation under Award No. EPS-0903806 and matching support from the
State of Kansas through the Kansas Board of Regents.
Case Study: Sheridan Co, KS
Estimated VMP (inverse demand ) for water

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