EE10: Demand and welfare theory

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EE10 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

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Last two weeks

• International externalities
• Optimisation analysis
• Game-theory analysis
• Acid rain
• Depletion of the ozone layer
• Climate change
• Pollution control CCS

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Economic Value

• Neo-classical revolution Value is relative,
  value measures demand versus supply, value is
  based on consumption and production
• Basis of valuation Peoples preferences, what
  people want
• Values depend on context
• Supply, demand
• Uncertainty Something that is uncertain is worth
  less, an uncertain loss is worth more
• Uniqueness Something that is unique is worth more

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What to value?

• Individuals can derive value from environmental
  goods from more sources than direct consumption
• Types of environmental services
• source of materials input fossil fuel, wood
  products, fish, water etc.
• life-support services liveable climatic regime,
  breathable atmosphere
• amenity services recreation, wildlife
  observation, scenic view, passive use values
• sink for the assimilation of wastes

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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

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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

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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

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Consumer demand theory -2

• Roys 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

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Constructing an ordinary demand function
x2
p1
I3
I2
I1
x1(p1,p2,M), demand for x1
C
Budget constraint
C
A
A
B
B
x1
x1
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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.

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Consumer demand theory -4

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

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Constructing a compensated demand function
p1
x2
I1
hx1(p1,p2,U1), demand for x1
C
C
A
A
B
B
Budget constraint
x1
x1
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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

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Income and price effects
x2
e/p21
A
Price effect
e/p22
B
Income effect
C
I1
I0
D
M
x1
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Surplus from ordinary and compensated demand
p1
If AB is an ordinary demand function like
x1(p1,p2,M) Consumer Surplus ABCD-BCDEABE
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
B
p1
C
D
x1
x1
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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
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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

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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)

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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

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Ordinary and compensated demand Welfare effects
p1
Compensated variation ABEG Consumer Surplus
AEFB Equivilent variation ADFB gt If p decreases
CVltDCSltEV
hx1(p1,p2,U0)
Compensated demand
hx1(p1,p2,U1)
E
A
D
p01
F
x1(p1,p2,M)
p11
B
G
Ordinary demand
x1
x01
x11
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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
• Well 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

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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, Roys identity relates x and v

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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

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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

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Restricted compensated demand
p1
A
Choke price
The income equivalent or marginal WTP for a
change in q ABC
B
C
p1
hx1(p1,q0,U1), initial demand for x1
hx1(p1,q0 Dq ,U1), demand for x1 after increase
in q
D
x1
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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)

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Measures of changes in welfare for an
environmental good
Expenditure on private good x, M
D
ES/px
If q0 increases to q1, income has to be reduced
by CS/p to keep the same utility
B
M
Mpxx
A
U2
CS/px
U1
C
U0
q0
q1
Quantity/quality of environmental good q
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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 individuals 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

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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)