Replaced with revised version of poster on 07/23/10.Production Economics, Resource /Energy Economics and Policy,

Alston, Julian M.

Fuller, Kate B.

Sanchirico, James N.

English

Research Papers in Economics

The Benefits and Costs of Alternative Policies for the Management of Pierce's Disease: 
A Case Study of the Blue-Green Sharpshooter in the Napa Valley
Kate Fuller, Julian Alston, and James Sanchirico
Kate Fuller is a Ph.D. candidate in the Department of Agricultural Economics, University of California, Davis.  Julian Alston is
a Professor of Agricultural Economics,  and Chair of the Robert Mondavi Institute’s Center for Wine Economics, 
University of California, Davis.  James Sanchirico is a Professor in the Department of Environmental Science and 
Policy, University of California, Davis, and a Non-Resident Fellow at Resources for the Future.
Poster prepared for presentation at the Agricultural & Applied Economics Association 
2010 AAEA,CAES, & WAEA Joint Annual Meeting, Denver, Colorado, July 25-27, 2010
Copyright 2010 by Kate Fuller, Julian Alston, and James Sanchirico. All rights reserved. 
Readers may make verbatim copies of this document for non-commercial purposes by any 
means, provided that this copyright notice appears on all such copies.The Benefits and Costs of Alternative Policies for the Management of Pierce's Disease:
A Case Study of the Blue-Green Sharpshooter in the Napa Valley
Kate Fuller     Julian Alston    Jim Sanchirico
kbfuller@ucdavis.edu            jmalston@.ucdavis.edu          jsanchirico@.ucdavis.edu
Image:  Anthony Gould
2 α
2
N N N


Model: We examine how neighboring vineyard owners affect each other through 
their control choices. Each vineyard owner seeks to maximize profit, subject to PD 
damage that depends on  given control choices of nearby vineyards.  Each grower 
faces the following maximization problem, where p represents the price of grapes, AB  
is bearing vines, Y is yield per vine, w(s) is the cost function for PD control, w(I) is the 
cost function for vine replacement, and ρ is the discount rate.
This maximization is subject to the following state equations for nonbearing and 
bearing vine stocks, respectively.   ANB  is the number of nonbearing vines, μ is the 
percentage of vines that move from nonbearing to bearing each year, N measures the  
BGSS stock, and di i the damage those insects inflict on nonbearing and bearing stocks, 
respectively.  η is the death rate for vines that die of old age. 
Total land is fixed, which constrains the total  number of vines a grower has.  In the 
following equation,  a converts vine count to acreage.
Additionally, the following equation of motion describes the insect population. Control 
(S) changes the population carrying capacity:
,,
ρ
0 max p Y ( ) ( )  
I S N i i i
Bt A w S w I e dt
     
Napa
Results:  We utilize quadratic cost functions for vine replacement and revegetation. 
Parameters were derived from the field interviews.  We solve for steady-state optimal 
control, insect population, and vine replacement in cooperative and non-cooperative 
scenarios.  Note that these two growers receive different prices for their grapes; 
Grower 2’s are higher-valued than Grower 1’s.  
Under these assumptions, we find that:
•Revegetation will be used to a greater extent under the cooperative regime than a 
non-cooperative one.  Growers 1 and 2 will revegetate four and three percent more 
than they would in the non-cooperative case, respectively.
•Sharpshooter counts will be lower in the cooperative regime than in the non-
cooperative one. Growers 1 and 2 will have four and three percent fewer sharpshooter 
than they would in the non-cooperative case, respectively.
•Replacement due to vine death will be less under the cooperative regime than this 
non-cooperative one. This effect is relatively small; Growers 1 and 2 will replace fewer 
than one percent less vines than they would in the non-cooperative case.  
We have graphed the difference in cooperative versus noncooperative outcomes for 
two growers, one who receives a relatively high crush price, and one who receives a 
relatively low crush price.  
0.01 β ; 0 β 1 S     
Abstract:  Pierce’s Disease  poses a deadly threat to California wine grapes.  
It is spread by xylem-feeding insects called sharpshooters.  In addition to direct 
interest  in the specific case, we aim to gain more general insight into the 
economics of Pierces Disease in California as a whole by studying PD as vectored 
by the Blue-Green Sharpshooter (BGSS, Graphocephala atropunctata) in the 
Napa Valley, where it has been endemic for many years.  
In the Napa Valley, methods of control include riparian revegetation,  green 
fencing, and pesticide application.  Some studies suggest that benefits from both 
revegetation and green fencing exceed the costs.  However not all vineyards opt 
to use these controls, suggesting that previous studies may have failed to 
capture some aspects of the problem, including:
• Differences between properties
• Interaction between neighbors
• Large up-front costs 
• Perennial crop, revegetation and 
green fence plants
We have developed a model of pest and disease 
management to study the role of interaction between 
neighboring growers as it affects the private and social 
optimal management strategy.  Using the model, we can 
simulate grower responses to  prices of pest and disease 
control, vine replacement, and crush.  The model is also 
developed in such a way such that we can specify different 
types of controls: (1) change in the amount of riparian habitat 
BGSS can occupy (the carrying capacity for the insects) due to  riparian re-
vegetation or (2) a  pesticide application that kills the insects directly.
We calibrate the model using information from interviews with vineyard 
managers.  Seven vineyard managers were interviewed using a process called 
“participatory mapping” to gain insight into how they make decisions regarding 
management of PD in different areas of their vineyard.
A
Parameter Explanation Given value
wS Unit cost of control ($/vine) 6
wI Unit cost of investment ($/vine) 11
p1 Crush price of grapes for Grower 1 ($/ton) 4000
p2 Crush price of grapes for Grower 2 ($/ton) 8000
dNB Damage per insect for non-bearing vines (transmission rate) 0.05
dB Damage per insect for bearing vines (transmission rate) 0.05
α Number of live offspring produced in one year by an adult female sharpshooter 25
β Measure of control effectiveness 0.03
Y Yield/vine (tons) 0.00382
a Acres/vine (acres) 1/1555
Scale unit at which the problem is solved (acres) 15
ρ Discount rate 0.04
μ Annual rate of vine maturity from non-bearing to bearing 0.2
η Annual non-PD death rate  0.02
A
A
a( ) NB B A A A 
1
1
μd
μ d η
NB NB
B NB B
A I A N
A A N A
  
  
Image:  Allen Lew
Focusing on two vineyard blocks, 
one with high PD incidence and 
one with relatively little, 
respondents were asked to 
sketch onto aerial images of 
those blocks where and how they 
manage PD and the associated 
costs over the space of the block.  
These interviews have allowed us 
to parameterize, test, and extend 
the bio-economic model, which 
will be used to understand and 
predict grower behavior under 
different scenarios, such as the 
introduction of a better-
performing control technique, a 
dramatic increase in PD, or PD 
spread by other vectors with 
different characteristics.
13
14
15
16
Grower 1 (Low Price) Grower 2 (High Price)
Revegetation
Coop
Non-Coop
95
100
105
110
115
Grower 1 (Low Price) Grower 2 (High Price)
Sharpshooter Population
Coop
Non-Coop
433
434
435
Grower 1 (Low Price) Grower 2 (High Price)
Vine Replacemnt
Coop
Non-Coop

The Benefits and Costs of Alternative Policies for the Management of Pierce's Disease: A Case Study of the Blue-Green Sharpshooter in the Napa Valley

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