Pollution and development

The model

We consider the following simple model:

We have one country and the rest of the world. In each country there is a representative consumer with the following utility function:

where:

*c _{p}* is the consumption

*c _{c}* is the consumption of good

*e* is the emission level;

q is the parameter who indicate the elasticity of preferences for pollution intensive good, with .

We suppose that p is the pollution intensive good and its production is associated with emission. *c* is the "clean" good with no level of emission.

*e = x _{p} *

where *x _{p}* is output of good

The production possibility frontier in any given country is linear, and is given by:

*x _{p} + x_{c} = P *

where *P* is the total capital stock (including human capital) of the country. For simplicity we assume the frontier have the same slope of 1 in each country. (In this case we neutralise all comparative advantages considerations.)

We assume too that in each country there exists a system of taxes and transfers which allows the government to implement the first-best allocation.

Case I.

First, we consider the solution in absence of trade. In this case we have *c _{p} = x_{p}* and

The solution is given by the following problem:

The first order condition is given by:

Its easy to see that the solution of this problem there exists.

It is clear from the previous equation that:

That means: emission levels monotonically increase with output.

Case II

Let us now consider what happens when that country is able to trade with the rest of the world. Let *p _{p}* the world price for the pollution intensive good and

Then each individual country maximises *U* subject to some restrictions.

We solve this problem in two steps.

Conditional on *R*, the problem solutions are:

*c _{c} = (1 - q
) R*

c_{p} = q
R / p_{p}

Substituting in (2) we have the problem:

Solving this problem we have the following solution:

a) **If P ³
(p_{p} –1) / b
then x_{p} = 0.** The country fully specialises in "clean" good production and imports the pollution intensive good.

b) **If **. **The country produce both goods**. We observe that , so the income rises, the emission level fall. This is because in that range it pays to give up part of extra income to produce less pollution intensive goods.

c) **If then x_{p} = P . The country fully specialises in p good**. It will produce more of it as it gets richer, so that > 0.