Transcript Water Resource Economics

Economic Analysis of
Alternative Water Plans:
Water Resource Economics
Water Resources Planning and
Management
Daene C. McKinney
River Basin Planning
𝑻
𝑴𝒊𝒏𝒊𝒎𝒊𝒛𝒆 𝒁 =
𝑾𝑴
𝒕=𝟏
S.T.
𝑻𝑴,𝒕 − 𝑿𝑴,𝒕
𝑻𝑴,𝒕
𝟐
+ 𝑾𝑰
𝑻𝑰,𝒕 − 𝑿𝑰,𝒕
𝑻𝑰,𝒕
𝑺𝒕+𝟏 = 𝑺𝒕 + 𝑸𝒕 − 𝑹𝒕
𝑺𝒕 ≤ 𝑲
𝟐
+ 𝑾𝑷
𝑻𝑷,𝒕 − 𝑿𝑷,𝒕
𝑻𝑷,𝒕
𝟐
Inflow
Qt
•
–
•
Benefits: Try to meet targets
Hydropower
–
wM
wI
wP
TM,t
TI,t
TP,t
St
Benefits: Try to meet targets
Benefits: Try to meet targets
weight for Municipal demand
weight for Irrigation demand
weight for Recreation
monthly target for municipal demand
monthly target for irrigation demand
monthly target for recreation
K1
Rt
Irrigation Water Supply
–
•
Reservoir
Municipal Water Supply
Municipal
Losses
Gains
Irrigation
Environmental
Flow
ZI
penalty for missing
target in month t
minimum
target
TI,t
release
XI,t
Decision Making
• Developing and managing water resources systems involves making
decisions.
• Modeling and data management tools can contribute to the information
needed to make informed decisions.
• Decisions in water resources management inevitably involve making
tradeoffs – compromising – among competing opportunities, goals or
objectives.
• One of the tasks of water resources system planners or managers involved
in evaluating alternative designs and management plans or policies is to
identify the tradeoffs, if any, among competing opportunities, goals or
objectives.
• It is then up to a largely political process involving all interested
stakeholders to find the best compromise decision.
System Performance Criteria
• Measures indicating just how well different management plans and
policies serve the interests of all stakeholders are typically called system
performance criteria
• B/C framework
– Convert impacts into a single monetary metric
– Find the plan that maximizes benefits vs costs.
– Does not address distributional issues of who benefits and who pays, and by how much.
• Water resources planning and management takes place in a multi-criteria
environment
• Stakeholders – individuals or interest groups who have an interest in the
outcome of any plan
• Quantification of an objective is the adoption of some quantitative scale
that provides an indicator for how well the objective would be achieved
Economic Criteria
• Water resources system development and management is often
motivated by economic criteria.
• Two economic concepts: scarcity and substitution.
– Scarcity - supplies of natural, synthetic and human resources are limited. Hence people
are willing to pay for them. They should therefore be used in a way that generates the
greatest return, i.e. they should be used efficiently.
– Substitution - individuals, social groups and institutions are generally willing to trade a
certain amount of one objective value for more of another
Objective for Ag, Muni and
Hydropower Water Use
• Maximize economic profit from water supply for irrigation,
M&I water use, and hydroelectric power generation, subject
to institutional, physical, and other constraints
Z = AG(wag ) + å[Muni(wmuni,t ) + Power(w power,t )]
t
Objective for Agricultural Water Use
• Profit from agricultural demand sites = equal to crop revenue
minus fixed crop cost, irrigation technology improvement
cost, and water supply cost
é
ù
Ag(wag,t ) = Aê pY (å wag,t ) - FC - TCú - Cw å wag,t
ë
û
t
t
A
p
FC
TC
Cw
wag
harvested area (ha)
crop price (US$/mt)
fixed crop cost (US$/ha)
technology cost (US$/ha)
water price (US$/m3)
water delivered to demand sites in growing season (m3)
Objective for Municipal Water Use
• Benefit from industrial and municipal demand sites is
calculated as water use benefit minus water supply cost
a
é
ù
w0 p0 êæ wmuni,t ö
Muni(wmuni,t ) =
ç
÷ + 2a +1ú - Cw wmuni,t
(1+ a ) êëè w0 ø
úû
Muni(w)
wmuni,t
w0
p0
e

benefit from M&I water use (US$),
municipal water withdrawal in period t(m3)
maximum water withdrawal (m3)
willingness to pay for additional water at full use (US$)
price elasticity of demand (estimated as -0.45)
1/e
Objective Function for Hydropower
Water Use
• The profit from power generation
Power(wturbine, t ) = ( Ppower - C p ) å Pt (wturbine,t )
t
Pt
wturbine,t
Ppower
Cp
Power production for each period (KWh)
Water passing turbines for each period (m3)
Price of paid for power (US$/KWh)
Cost of producing power (US$/KWh)
Consumers
• Purchase “goods” and “services” x  ( x1, x2 ,..., xn )
• Have “preferences” expressed by “utility” function
u(x)  u( x1, x2 ,..., xn )
Good 2 x2
Indifference curve
u ( x1, x2 )
Better Bundles
Increasing
utility
Worse
Bundles
u
x1
Good 1
Consumer’s Budget
• Consumers have a “budget”, expressed by a budget
constraint p1x1  p2 x2  m
Good 2
x2
m/p2
Unaffordable
bundles
Budget line
p1x1+p2x2=m
Slope = -p1/p2
Affordable
bundles
m/p1
x1
Good 1
Consumer’s Problem
Maximize u ( x )
subject to
p x  m
x0


L( x,  )  u ( x )    m   pk xk 


k 1
K
u
xk

pk
k  1,..., K
Purchase so that the ratio of marginal benefit
(marginal utility) to marginal cost (price) is equal
among all purchases
L
u

 pk  0, k  1,..., K
xk xk
K
L
 m   p k xk  0

k 1

u
m
The ratio (in dimensions of $/unit or shadow price)
is the Lagrange multiplier, the change in utility for a
change in consumer income
Consumer’s Problem (2 goods)
Maximize u ( x1, x2 )
subject to
p1x1  p1x1  m
Good 2
x2
Indifference curve
slope = MRS12
u
 p1  0
x1
u
  p2  0
x2
Optimal choice
MRS12 = -p1/p2
Budget line
slope = -p1/p2
x2*
Increasing
utility
m  ( p1x1  p2 x2 )  0
u
x1

p1
u
x2

p2
x1*
Solution: slope of budget line
equals slope of indifference
curve
x1 Good 1
Demand
• Solution to Consumer’s Problem gives
puschase amounts which aggregate to
demand
Price, p
Maximize u(x)
subject to
p×x £ m
Demand curve
x(p,m)
x³0
 x *  x *  p, m 
Quantity, x
Willingness-to-Pay
• Value - What is someone willing to pay?
• Suppose consumer is willing to pay:
–
–
–
–
$38 for 1st unit of water
$26 for 2nd unit of water
$17 for 3rd unit of water
And so on
Price,p p
Price,
40
38
CS = Net Benefit = 53
• If we charge p* = $10
– 4 units will be purchased for $40
– But consumer is willing to pay $93
– Consumer’s surplus is $53
30
26
WTP = Gross Benefit = 93
20
17
Total cost = 40
12
p*=10
Quantity, q
1
2
3
4
5
Quantity, x
Willingness-to-Pay
Market Prices – Revealed WTP
• Some goods or services are traded in markets
– Value can estimated from consumer surplus (e.g., fish, wood)
• Ecosystem services used as inputs in production (e.g., clean
water)
– Value can be estimated from contribution to profits made from the
final good
• Some services may not be directly traded in markets
– But related goods that can be used to estimate their values are trade in
markets
• Homes with oceanviews have higher price
• People will take time to travel to recreational places
• Expenditures can be used as a lower bound on the value of the view or the
recreational experience
Firms
• Firms produce outputs from inputs (like water)
• Firm objective: maximize profit
input 2
output y
Input, x2
Production function
y = f(x)
Isoquant
f ( x)  y0
y2
y1
Slope = df/dx
Increasing
output
x
input
y0
Input, x1
input 1
Production Function
Y Ymax [a0  a1( x / Emax ) a2 ln(x / Emax )]
Ymax
b0 … b8
x
Emax
s
u
a0  b0  b1u  b2 s
a1  b3  b4u  b5s
a2  b6  b7u  b8s
= maximum yield (mt/ha)
= coefficients,
= irrigation water applied (mm)
= Max ET (mm)
= irrigation water salinity (dS/m)
= irrigation uniformity
8.00
II
Output, y (ton/ha)
I
III
6.00
4.00
2.00
0.00
0
5,000
10,000
Input, x (m3/ha)
15,000
20,000
Profit
•
•
•
•
Output
Input
Revenue
Cost
y  f (x )
x
R  py
N
C   wn xn
n 1
  R C
• Profit
N
  pf ( x )   wn xn
n 1
The Firm’s Problem
N
Maximize p ( p,w) = pf (x1 ,..., x n ) - å wn x n
n=1

f
0  p
 wn , n  1,..., N
xn
xn
y
Isoprofit line
= py – wx
slope = w/p
df/dx= w/p
wn
f


xn
p
n  1,..., N
y*
/w
Prod. Fcn.
y = f(x)
slope = df/fx
x*
x
Revenue (1) Price-setting Firm
Revenue
R  py
• Marginal Revenue
dR R R dp
dp


 p y
dy y p dy
dy
(1)
•
Increase in output (dy) has two effects
1.
2.
(1) Adds revenue from sale of more units, and
(2) Causes value of each unit to decrease
(2)
Revenue (2) Price-taking Firm
Revenue
•
R  py
Competitive firm: p is constant
• Marginal Revenue
– derivative WRT y
dR d ( py)

p
dy
dy
Example
p
Linear demand function
Revenue
py = ay – by2
Demand function
p = a - by
a
p( y)  a  by
b
a/b
p
• Revenue
R  py  ay  by 2
Demand function
p = a - by
a
b
2b
a/b
y*
y
Revenue
• Marginal prevenue
py = ay – by
Demand function
a
– slope
is twice
of demand
p = a -that
by
dR
 a  2by
b
dy
y*
y
Marginal
Revenue
= a – 2by
2
y
y
Marginal
Revenue
= a – 2by
Revenue
py = ay – by2
a
a/b
y*
y
a
2b
y
a/2b
y
a/2b
y
Cost Functions
N
Minimize  wn xn
n 1
subject to
f ( x1,..., x N )  y 0
L
f
 wn  
 0 n  1,..., N
xn
xn
L
 f  y0  0

f
wm
xm

wn f
xn
Cost Functions
Total Cost (fixed and variable costs)
TC ( y )  min  w  x : y  f ( x )
TC ( y)  FC  VC ( y)
Average cost (cost per unit to produce y units)
AC 
TC ( y )
y
Marginal cost (cost to produce additional unit)
MC 
dTC dVC

dy
dy
Example (1) Price-taking Firm
• How much water should a water company produce
Price &
Cost
MC
Maximize  ( y)  py  TC ( y)
d
dp
dTC
0
y p
dy
dy
dy
AC
p*
p = MC
MR( y)  p  MC ( y)
p  MC
y*
y
Product
Example (2) Price-setting Firm
• Firm influences market price
• Choose production level and price to maximize profit
Maximize  ( y)  py  TC ( y)
d
dp
dTC
0
y p
dy
dy
dy
Price &
Cost
MC
Demand
MR
AC
pm
p = MC
p*
MR ( y ) 
dp
y  p  MC ( y )
dy
MR( y)  MC ( y)
MR = MC
ym
y*
y
Objective Function for Agricultural
Water Use
• Profit from agricultural demand sites = equal to crop revenue
minus fixed crop cost, irrigation technology improvement
cost, and water supply cost
é
ù
Ag(wag,t ) = Aê pY (å wag,t ) - FC - TCú - Cw å wag,t
ë
û
t
t
A
p
FC
TC
Cw
wag
harvested area (ha)
crop price (US$/mt)
fixed crop cost (US$/ha)
technology cost (US$/ha)
water price (US$/m3)
water delivered to demand sites in growing season (m3)
Y (wag ) = Ymax [a0 + a1 (wag / Emax ) + a2 ln(wag / Emax )]
Objective Function for Municipal and
Industrial Water Use
• Benefit from industrial and municipal demand sites is
calculated as water use benefit minus water supply cost
a
é
ù
w0 p0 êæ wmuni,t ö
Muni(wmuni,t ) =
ç
÷ + 2a +1ú - Cw wmuni,t
(1+ a ) êëè w0 ø
úû
Muni(w)
wmuni,t
w0
p0
e

benefit from M&I water use (US$),
municipal water withdrawal in period t(m3)
maximum water withdrawal (m3)
willingness to pay for additional water at full use (US$)
price elasticity of demand (estimated as -0.45)
1/e
Objective Function for Hydropower
Water Use
• The profit from power generation
Power(wturbine, t ) = ( Ppower - C p ) å Pt (wturbine,t )
t
Pt
wturbine,t
Ppower
Cp
Power production for each period (KWh)
Water passing turbines for each period (m3)
Price of paid for power (US$/KWh)
Cost of producing power (US$/KWh)
Combined Objective Function for Ag,
M&I and Hydropower Water Use
• Maximize economic profit from water supply for irrigation,
M&I water use, and hydroelectric power generation, subject
to institutional, physical, and other constraints
Z = AG(wag ) + å[Muni(wmuni,t ) + Power(w power,t )]
t