Heterogeneity Revisited
Clarification for EEP101/Econ125
The following handout is intended to clarify the concept of heterogeneity among
producers and the effect of particular policy interventions in this context.
I will be using
the same example that I attempted to present in section last week.
Setup
The story goes as follows: There are three firms, each with different demands for
pollution.
This is a strange way of looking at the world, but it might be helpful to think
of pollution as an input to the production process.
In this case, the marginal benefit for
each firm to produce one more unit of pollution is like the extra amount of profit that they
earn by imposing one more unit of pollution on society.
If you consider figure 1 (attached, since I can’t figure out how to draw it on the
computer), you’ll see a three firm example.
Note that firm 1 produces less pollution at
any given price.
This means that he (probably she) is more efficient.
The big MB is just
the horizontal sum of all of the firms marginal benefits curves, and the area under it
represents the total benefits (profits) to the industry from producing at point Q.
As always, the socially optimal point is found be setting marginal benefits equal to
marginal social cost.
We can reach this point in one of several ways: by taxing,
subsidizing, a uniform standard, or through tradable permits.
We will go through these
cases, but first, let’s set up the math so that we can go back and forth between algebra and
graphs.
The three marginal benefits are given by:
mb
1
= 75  (5/4)q
1
mb
2
= 75  q
2
mb
3
= 75  (3/4)q
3
Remember, q represents the amount of pollution here.
To figure out MB, we need to sum
these things horizontally.
This requires taking the inverse of these functions, i.e., solving
q in terms of mb.
The inverses are:
q
1
= 60  (4/5)mb
1
q
2
= 75  mb
2
q
3
= 100  (4/3)mb
3
If you sum them up, you get the big Q of pollution for the whole industry.
Q = 235  (47/15)MB
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 Spring '07
 Wood
 Economics, producer, marginal social cost, marginal benefits

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