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.

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

• This consumer maximises the utility of a bundle of goods x, with prices p, and income M

• This solves to the ordinary or Marshallian demand function

• Substituting the expression for xi gives the indirect utility function

– this gives you the highest level of utility attainable, given prices p and income Y

max ( ) s.t. ; 0i iu u X p x M x

( , )i ix x P M

( )u u X

( , )u v P M

Consumer demand theory -2

• Roy‘s identity relates x and v:

• 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

( , ) i

i

v px P M

v M

Constructing an ordinary demand function

A

B

C

I1I2

I3

p1

C

A

B

x1(p1,p2,y), demand for x1

Budget constraint

x1x1

x2

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

• This solves to the compensated or Hicksian demand function

• 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.

1min s.t. ( ) ; 0i ie p x u X u X

1( , )e e P u M

Consumer demand theory -4

• Demand for the ith commodity is the derivative of the expenditure function to the price of i

1( , )i i

i

eh h P u

p

Constructing a compensated demand function

A

B

C

I1

C

AB

hx1(p1,p2,U1), demand for x1

Budget constraint

p1

x1 x1

x2

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

A

B

x2

x1

Price effect

e/p21

Income effectC

D

I1I0

e/p22

M

Surplus from ordinary and compensated demand

A

B

p1

x1

If AB is an ordinary demand function like x1(p1,p2,M):

Consumer Surplus= ABCD-BCDE=ABE

Ep*1

x*1

If AB is a compensated demand function like hx1(p1,p2,U1) the area under the curve correspond to changes in constant utility expenditures

CD

Ordinary and compensated demand - 3

A

B

hx1(p1,p2,U1

)

x1(p1,p2,M)

p1

x1

hx1(p1,p2,U0

)

Ordinary demand

Compensated demand

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

1 1 1 2 1 2

0 1 0 0 1 0( , ) ( , , ) ( , , )x x x x x xCV p p e p p u e p p u

1 1 1 2 1 2

0 1 0 1 1 1( , ) ( , , ) ( , , )x x x x x xEV p p e p p u e p p u

Ordinary and compensated demand: Welfare effects

B

hx1(p1,p2,U1

)

x1(p1,p2,M)

p1

x1

hx1(p1,p2,U0

)

Ordinary demand

Compensated demand

A

G

F

DE

x01 x1

1

p11

p01

Compensated variation: ABEG

Consumer Surplus: AEFB

Equivilent variation: ADFB

=> If p decreases CV<CS<EV

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 utility

• This consumer maximises the utility of a bundle of goods X, with prices P, and income M

• This leads to restricted ordinary demand functions

• and a restricted indirect utility

• Again, Roy‘s identity relates x and v

max ( , ) s.t. ; , 0i ii

u X q px M q X

( , , )i ix x P M q

( , , )u v P M q

( , )u u X q

Restricted demand - 2• The dual of the problem: Minimising expenditure

• This leads to the expenditure function function

• The Hicks-compensated demand function for changes in prices is

• The Hicks-compensated inverse demand (marginal WTP) for changes in q is

• Rearranging the equation yields the compensating demand for q

1( , , )e P q u M

1( , , )i i

i

eh h P q u

p

1min s.t. ( , ) ; 0i ie p x u X q u q

1( , , )xq q

e P q uw p

q

1( , , )q x qq h P p u

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

Choke price

p1

x1

p*1 hx1(p1,q0,U1), initial demand for x1

C

D

A

B

hx1(p1,q0 +q ,U1), demand for x1 after increase in q

The income equivalent or marginal WTP for a change in q: ABC

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

• U0 results from (P,q0,M)

0 1 0 0 1 0( , ) ( , , ) ( , , )CS q q e P q U e P q U

0 1 0 1 1 1( , ) ( , , ) ( , , )ES q q e P q U e P q U

Measures of changes in welfare for

an environmental good

A

B

C

D

U1

U2

q0

q1

M M=pxx

Expenditure on private good x, M

Quantity/quality of environmental good q

U3CS/px

ES/px If q0 increases to q1, income has to be reduced by CS/p to keep the same utility

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