requires solving for a new tax to induce the Pareto-optimal level of phosphorous
loading into the lake.
This paper therefore considers the case where society’s preferences for the
state of the lake are characterised by two distinct welfare functions. This can
be thought of as two types of communities that share the use of the lake where
one type of community is predominantly agricultural and benefits more from
higher phosphorous loading, and the other, a green community, has a higher
preference for an oligotrophic lake.
As noted above, the shallow lake presents a hysteresis in its response to
phosphorous loading. Its biological function remains the same as in the case
with a single welfare function. Under the constraint of the lake’s response to
phosphorous, each community will aim to optimize its welfare according to one
of two welfare functions, thus giving rise to a Nash equilibrium different from
the single-welfare function case. The Pareto-optimal amount of phosphorous
loading will also be different in the two-function case, and therefore so will the
tax required to induce each community to behave such a way as to attain a
Pareto outcome. The first part of our analysis finds these results.
In the second part, lobbying by the two types of communities and its impact
on the optimal tax policy is assessed. It is shown that as a result of lobbying,
the optimal tax policy may not be implemented and further, that even when
the tax falls only slightly short of the optimal tax, the hysteretic property of
the lake may lead to its being in a eutrophic state.
Several articles explore the consequences of rent-seeking on environmental
policy (Damania, 1999; Wilson and Damania, 2005) and on the optimal tax rate
in particular (Lee, 1985; Brooks and Heijdra, 1987). However, there are cur-
rently no publications that combine the dynamics of the shallow lake, optimal
taxation and the impact of rent-seeking behaviour on the application of this
policy. The following work provides new results and insights into why socially
optimal tax policy may often not be implemented.
We begin by describing the lake dynamics upon which this analysis is based.
2 Shallow Lake Dynamics
How are shallow lakes different from deep lakes? In summer months, the wa-
ter of deep lakes stratifies into layers of different temperatures. During these
months, nutrients are lost from the warm upper layers (epilimnion) to the colder
deeper layers (hypolimnion), where they sink to the bottom into the sediments
and remain segregated from the epilimnion until winter when the water column
of the entire lake becomes mixed again.
Shallow lakes are different from deeper lakes because they tend to be polymic-
tic, i.e. have a mixed water column most of the time. Shallow lakes can have
a small or large surface, and the proportion of their water that is in contact
with sediments makes them function differently from deep lakes. In particular,
the rate of recycling of nutrients from sediments into the water is much higher.
This means that more nutrients are available to consumers, including to micro-
organisms such as algae. As a result, contrary to deep lakes where vegetation