Download Valuation 2: Environmental Demand Theory

Valuation 2 and 3:
Demand and welfare theory
• What is so special about environmental goods?
• Theory of consumer demand for market goods
• Welfare effects of a price change: Equivalent
variation versus compensating variation
• Consumer demand for environmental goods
• Welfare effects of a quantity change: Equivalent
surplus versus compensating surplus
• Theory and practise
Last week
•
•
•
•
Price and Value
Total Economic Value
Why and what to value?
Uses of economic valuation
Why valuation?
• We must make choices about how to
manage the human impact on natural
systems
• Greater use of a particular environmental
service or greater protection of a specific
natural system results in less of something
else (trade-off)
• To make the most of scarce resources we
must compare what is gained from an
activity with what is sacrificed by
undertaking that activity
• Why? To assess the net impact of changes
What is so special about
environmental goods and services?
• In economics the criterion for assessing the net impacts
(„benefits“ and „costs“ ) is the well-being of the members of
society
• Well-being is defined as the individuals‘ preferences for
goods
• Preferences are typically represented through demand
functions
– Changes in well-being can be inferred by changes in prices or
quantity
• Problem with environmental goods: no markets exist
– Individuals have preferences nevertheless
• Changes in well-being are derived by individuals’
– max. willingness to pay for gains or (WTP)
– min. willingness to accept compensation for losses (WTA)
• Prices and marginal WTP or WTA are equivalent
Consumer demand theory:
Market goods
• Consider a consumer who has a utility function
u  u (X )
• This consumer maximises the utility of a bundle of goods x,
with prices p, and income M
max u  u (X ) s.t.
p
i
 xi  M ; x  0
• This solves to the ordinary or Marshallian demand function
xi  xi (P , M )
• Substituting the expression for xi gives the indirect utility
function
u  v (P , M )
– this gives you the highest level of utility attainable, given prices
p and income Y
Consumer demand theory -2
• Roy‘s identity relates x and v:
v pi
xi (P , M )  
v M
• That is, the derivative of indirect utility
with respect to the ith price yields the ith
demand function, after normalising by the
marginal utility of income
Constructing an ordinary demand function
x2
p1
I1
I2 I3
x1(p1,p2,y), demand for x1
C
Budget constraint
C
A
A
B
B
x1
x1
Consumer demand theory -3
• An alternative to generate a demand curve is to keep utility
constant instead of income
• Here the consumer is assumed to minimize total expenditure
to achieve a given level of utility at price level P
min e   pi  xi s.t. u (X )  u 1 ; X  0
• This solves to the compensated or Hicksian demand function
e  e (P , u 1 )  M
• This gives the quantity demanded as a function of price and
utility
• Income is of no consequence; as prices change, expenditures
are adjusted to maintain constant utility.
Consumer demand theory -4
• Demand for the ith commodity is the
derivative of the expenditure
function to the price of i
e
1
 hi  hi (P , u )
pi
Constructing a compensated demand function
x2
p1
I1
hx1(p1,p2,U1), demand for x1
C
C
A
A
B
Budget constraint
x1
B
x1
Ordinary and compensated
demand
• We derived ordinary and compensated demand
functions
• Ordinary demand functions bundle income and
price effects together
• Compensated demand function do not have this
problem, but look at price effects alone
• To evaluate the effect of a governmental policy
that changes relative prices we want to examine
the price effect only
• Typically, economists estimate ordinary demand
functions, as utility cannot be observed
Income and price effects
x2
e/p21
A
e/p22
Price effect
B
C
Income effect
I0
D
M
I1
x1
Surplus from ordinary and compensated demand
p1
If AB is an ordinary demand function like x1(p1,p2,M):
Consumer Surplus= ABCD-BCDE=ABE
A
If AB is a compensated demand function like
hx1(p1,p2,U1) the area under the curve
correspond to changes in constant utility
expenditures
E
p*1
D
B
C
x*1
x1
Ordinary and compensated demand - 3
p1
hx1(p1,p2,U0)
Compensated demand
hx1(p1,p2,U1)
A
B
x1(p1,p2,M)
Ordinary demand
x1
Ordinary and compensated
demand - 4
• Properties of both demand functions are
related
• We observe ordinary demand functions,
but we are interested in compensated
demand functions – the latter can be
derived from the former if agents are
rational, and even then it involves many
steps including integration
Welfare effects of price
changes
• Consider price fall P*  P#
• Willingness to pay (WTP) to secure price fall is
known as compensating variation (CV)
• Willingness to accept compensation (WTAC) to
forego price fall is known as equivalent variation
• There are gains and loss, so four measures (EV)
– Price decreases
• WTP to secure a gain (CV)
• WTAC to forego a gain (EV)
– Price increases
• WTP to prevent a loss (EV)
• WTAC to tolerate a loss (CV)
Welfare measures
• Compensating variation is the quantity of
income that compensates consumers for a
price change, that is, returns them to their
original welfare
• Equivalent variation is an income change
that yields the same utility change as the
price change
• Both terms can be defined using the
expenditure function
CV ( px01 , px11 )  e ( px01 , px2 , u 0 )  e ( px11 , px2 , u 0 )
EV ( px01 , px11 )  e ( px01 , px2 , u 1 )  e ( px11 , px2 , u 1 )
Ordinary and compensated demand:
Welfare effects
p1
Compensated variation: ABEG
Consumer Surplus: AEFB
hx1(p1,p2,U0)
Equivilent variation: ADFB
=> If p decreases CV<DCS<EV
Compensated demand
hx1(p1,p2,U1)
p01
E
A
D
F
p11
B
x1(p1,p2,M)
G
Ordinary demand
x01
x11
x1
Consumer demand theory:
Environmental goods
• Often demand for environmental
commodities is only indirectly observed
• People change their behaviour in response
to changes in the environment, but do not
purchase environmental quality directly
• We‘ll repeat the analysis above, but now
assume that only n-1 goods are directly
traded; the nth good (named q) is the
environmental commodity of interest
Restricted demand
• The environmental good q affects individuals
u  u (X , q )
utility
• This consumer maximises the utility of a bundle of
goods X, with prices P, and income M
max u (X , q ) s.t.
px
i
i
i
 M ;q , X  0
• This leads to restricted ordinary demand
xi  xi (P , M, q )
functions
• and a restricted indirect utility
u  v (P , M, q )
• Again, Roy‘s identity relates x and v
Restricted demand - 2
• The dual of the problem: Minimising expenditure
min e   pi  xi s.t. u (X , q )  u 1 ;q  0
• This leads to the expenditure function function
e (P , q , u 1 )  M
• The Hicks-compensated demand function for changes in
prices is
e
 hi  hi (P , q , u 1 )
pi
• The Hicks-compensated inverse demand (marginal WTP) for
changes in q is
e (Px , q , u 1 )
wq  pq  
q
• Rearranging the equation yields the compensating demand
for q
q  hq (Px , pq , u 1 )
Restricted demand - 3
• But...
• we can determine how expenditures change with q
for some price of good x and implicitly defining a
demand function for q only if we assume weak
complementarity
• That is, if the demand for good x drops to zero,
then demand for good q goes to zero as well and
marginal changes in q no longer affect expenditure
• Example: if swimming is too expensive, water
quality is irrelevant
Restricted compensated demand
p1
A
Choke price
The income equivalent or
marginal WTP for a change in
q: ABC
B
p*1
C
hx1(p1,q0,U1), initial demand for x1
hx1(p1,q0 +Dq ,U1), demand for x1 after increase in q
D
x1
Welfare effects of quantity
changes
• Measures of „surplus“ instead of „variation“ when
consumers are not free to vary the quantity of q
• In case of quantity changes, compensating and
equivalent surplus are defined as
CS (q0 , q1 )  e (P , q0 ,U0 )  e (P , q1,U0 )
ES (q0 , q1 )  e (P , q0 ,U1 )  e (P , q1,U1 )
• U0 results from (P,q0,M)
Measures of changes in welfare for an
environmental good
Expenditure on
private good x, M
D
ES/px
M
If q0 increases to q1, income has to
be reduced by CS/p to keep the same utility
B
A
CS/px
C
q0
M=pxx
q1
U1
U2
U3
Quantity/quality of
environmental good q
WTP and WTAC
• If the good is relatively unimportant ES and CS are roughly
the same
• If environmental goods are relatively scarcer than market
commodities, one may expect the compensating
variation/surplus (WTP) to be smaller than the equivalent
variation/surplus (WTAC) for improvements
• Differences between WTP and WTAC are mainly due to
income effects
• People view gains and losses differently
– WTP is limited to an individual‘s income, WTAC is unbounded
– Confirmed by empirical studies, but not uncontested
– Implies that surveys, policies need to be carefully designed
• Income effects are small only if the good is of little value
relative to your overall wealth
Theory and practice
• Horowitz and McConnell collect 208
observations of WTP and WTAC from 45
studies
• For all studies, the average ratio
WTAC/WTP is 7.2 (0.9)
• However, for public or non-market goods,
the ratio is 10.4 (2.5)
• For ordinary goods, it is 2.9 (0.3)
• For money, it is 2.1 (0.2)
Methods for measuring
demand
• Indirect methods (use values)
– Surrogate market where we observe expenditures on a
related goods
– Infer information on the trade-off between money and
the environmental good
– Hedonic pricing
– Household production function approach
• Direct methods (use and non-use values)
– Hypothetical/constructed market
– Contingent valuation: “value contingent on there being a
market”
– Choice modelling