Defensive expenditures,
welfare and growth in a NorthSouth model
A. Antoci (University of Sassari)
S. Borghesi (University of Siena)*
Overview
• Object: link between environmental defensive
expenditures, welfare and growth
• Definition: expenditures that agents can do to
protect against the deterioration of the
environment they live in.
• Substitution mechanism: replace consumption of
“free” environmental public goods with that of
expensive private goods that may satisfy the
same needs.
• Examples: mineral water, double glazing, masks,
health expenditures, air conditioners…
urban sprawl
holidays in some tropical paradise
Overview
• Empirical estimations: Leipert and Simonis, 1989; Daly
and Cobb, 1990; Statistics Canada, 1998; Garrod and
Willis, 1999; United Nations, 2003.
↑Environmental
degradation
↑ Defensive
expenditures
↑ GDP
• Related literature: Antoci and Bartolini (1999, 2004);
Bartolini and Bonatti (2003); Antoci et al. (2008)
• a two-population game: North-South model
SET UP OF THE MODEL
• 2 hemispheres: North and South
• 4 goods:
– leisure (1-L)
– a free access (renewable) environmental good (E)
– good 1: a non-storable produced good that can be
consumed to satisfy basic non-environmental needs
(subsistence consumption)
– good 2: a non-storable produced good that can be
consumed as a substitute for the depleted environmental
good (substitution consumption)
• Goods 1 and 2 produced by labor alone
• Production depletes the renewable natural
resource
• To counterbalance such depletion agents may
increase their labor supply in order to afford the
substitution consumption
SET UP OF THE MODEL
• Each agent decides how much to work:
– Low (l) → subsistence consumption → Y1
– High (h) → substitution consumption →Y2
U l j = a * ln (1 - Ljl ) + b * ln Y1j + ln E j

j  N,S
U hN = a * ln (1 - LNh ) + b * lnY1N + ln E N  c * ES  d * Y2N

U hS = a * ln (1 - LSh ) + b * lnY1S + ln ES  e * Y2S


• Northern agents that work high can also
enjoy Southern environment
•
Call x (z) the share of agents that choose to
work high in the North (South): 0≤x≤1,0≤z≤1
1
z
0
•
1
Define the payoff differential between
working high and low in hemisphere j=N,S
U ( x, z )
j
•
x
j
j
 U h ( x, z )  U l ( x, z )
and assume the following “replicator
dynamics”:  x  x(1  x)U N ( x, z )


 z  z (1  z )U S ( x, z )
Dynamics along the sides
DYNAMICS AND WELFARE ALONG
THE SIDES OF THE SQUARE
Suppose z = 0.
• Call A the amount of natural resources that are left in the
North after production Y1.
A sufficiently low → hN-dominance
A sufficiently high → lN-dominance
• If A sufficiently low, Northern people want to go on holiday
to the South where the environment is better preserved,
therefore they are induced to work high. If A sufficiently
high, Northern agents do not have such an incentive,
therefore they prefer to work low and enjoy their
environment.
• If there exists a fixed point x  x0N  (0,1)
• then it is always: U N (0,0)  U N ( x0N ,0)  U N (1,0)
• where:
U ( x, z ) 
N
N
N
xU h ( x, z )  (1  x)U l ( x, z )
DYNAMICS AND WELFARE FOR
ALL VALUES OF x AND z
• If the dynamics of x and z are non trivial
(i.e. the time derivatives of x and z and are
not always positive inside the square),
then the point (0,0) Pareto-dominates any
other possible state (x,z) in the North
and/or in the South.
Intuition for the limit cycle:
Leonardo di Caprio and Phi-Phi
islands
if z is initially low (i.e. the Southern activity level
is low), the environment in the South is well
preserved and Northern agents are induced to
work high. As x increases, however, this
damages the Southern environment, leading to
an increase in z since more Southern agents
work high to afford defensive expenditures.
When z is high enough, working high is no
longer the best strategy for Northern agents,
therefore x decreases, which leads to a
reduction in z as well and so on.
Concluding remarks
• Environmental degradation induces individual defensive
expenditures that raise the activity level which, in turn, might
further increase environmental degradation.
• Both hemispheres may end up in a situation where everyone
works “too much”: people work harder to protect against
pollution, but they might be better-off by working less and
enjoining a cleaner world. This outcome may occur both for
“polar” values of x and z (along the square) and for all
possible values of x and z (inside the square).
• North-South interactions may also generate limit cycles in
the model
FUTURE RESEARCH:
• Positive effect of higher production on the environment (e.g.
technique effect)
• Positive effect of Northern production on Southern
environment (tourism)…..