Defensive expenditures, welfare and growth in a North- South 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, Defensive expenditures GDP Environmental degradation 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 Y 1 –High (h) substitution consumption Y 2 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): 0x1,0z1 Define the payoff differential between working high and low in hemisphere j=N,S and assume the following replicator dynamics: z x 0 1 1

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 Y 1. A sufficiently low h N -dominance A sufficiently high l N -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 then it is always: where:

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)…..