Economic Modelling for Environmental Applications

1
Economic Modelling for Environmental Applications

• Dr. Richard S.J. Tol
• Michael Otto Professor of Sustainability and
  Global Change
• Depts. GeoSciences Economics

2
The Course

• The theory and practice of economic modelling for
  environmental applications
• Ill show a number of basic economic tools, take
  you through the crucial assumptions, the
  necessary math, and the show how this can be used
  for environmental analysis
• Horses for courses, and dont let the better be
  the enemy of the good
• Prior knowledge calculus, environmental
  economics and management
• Reader

3
The Lectures

• Mon Free (data econometric models
  geographical economics)
• Tue 1100-1200 Consumer theory, incl.
  Valuation
• 1200-1300 Producer theory, incl. Env.
  Change
• 1400-1530 Input-output model, incl. LCA
• Wed 1330-1545 General equilibrium incl.
  Top-down v Bottum-up, Higher-order Impacts
• Thu 1300-1430 Solow growth, incl. carbon
  leakage
• 1500-1630 Ramsey growth, incl.
  efficient control
• Fri 1030-1200 New growth, incl.
  cost-effective control
• 1300-1430 Game theory, incl. optimal
  control

4
Utility Theory

• Consider a rational consumer, that is a consumer
  with complete, non-transitive (and hence
  connected) preferences
• Then, we can represent the choices of this
  consumer by
• Further, assume non-satiation
• Further, assume strict convexity

5
Utility Theory -2
6
Demand Theory

• The solution to
• is something like
• which can be rewritten as

7
Demand Theory 2

• A function is homogenous of degree a if
• The demand function is homogenous of degree zero
  since
• So
• There is no money illusion in the model, that is,
  absolute prices are irrelevant or everything is
  relative

8
Demand Theory 3

• The own/cross price elasticity of demand
• The income elasticity of demand
• A good is normal if eiy gt 0 (inferior)
• A good is luxury if eiy gt 1 (necessary)

9
Income Elasticity

• Income elast. domestic water withdrawal
• Sub-Saharan Africa 1.2
• India 1.0
• China 0.8
• Latin America 0.6
• Eastern Europe 0.2
• Western Europe 0.0
• That is, if people in China grow 1 richer, they
  consume 0.8 more water
• Western Europe is satiated
• In Africa, water is a luxury good

10
Demand Theory 4

• Homogeneity
• Assume ?1, a0, f(x)D(p,y)
• Divide by Di(p,y)

11
Demand Theory -5

• Consider a consumer who maximises the utility of
  a bundle of goods q, with prices p, and income Y
• This solves to the ordinary or Marshallian demand
  function
• And to the indirect utility function v(p,Y) this
  gives you the highest level of utility
  attainable, given prices p and income Y it is an
  optimal value function

12
Demand Theory -6

• 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

13
Restricted Demand

• Demand for environmental commodities is only
  indirectly observed. People change their
  behaviour in response to changes cq differences
  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 is the environmental commodity of interest.

14
Restricted Demand -2

• This leads to restricted ordinary demand
  functions and a
  restricted indirect utility function
• Roys identity implies
• The duality between prices and quantities

15
Consumer Theory

• Nice math, but one piles assumption on assumption
  to apply this to an environmental issue
• Seemingly innocuous assumptions can have rather
  strong implications
• At the same time, even with simple assumptions,
  things get very complicated very rapidly, for
  instance if one includes a non-market good ...

16
Reality

• Microeconomics assumes that people are rational,
  that is maximise utility
• Each of us knows several counter examples in
  which we or others acted in a particularly stupid
  way
• So, how can we assume rationality?
• First, rationality is about average behaviour
• Second, rationality is a simplification, as in
  any other model

17
Reality -2

• Third, rationality results from evolution
• Entrepeneurs that do not realise the maximum
  possible profit will be forced out of the market
  (eventually)
• Darwinian forces maximise fitness, economic
  forces maximise profit and utility
• (Perhaps the more debatable assumption is about
  the objective functions of the economic agents)
• Fourth, there is substantial empirical evidence
  that animals are rational

18
Reality -3

• Actually, agents do not maximise utility but
  expected utility
• This has been shown for animals (birds) in
  experiments, maximising expected net energy
  intake (i.e., food minus effort)
• This has also been shown experimentally for rats,
  maximising expected pleasure (with electronic
  stimulation of the pleasure lobs in the brain)

19
Reality -4

• Neuroscientists have shown experimentally that
  maximising expected utility (in this case,
  berry-berry juice) is hardwired in the brains of
  rhesus monkeys, demonstrating that the brain does
  not respond to the size of the stimulus, but
  rather to the size of the pay-off and the
  probability