sufficiently high, for the environmental policy to have a very high chance of
being implemented.
A perhaps more interesting result is that by proposing a tax level below the
one required to bring the lake back to a socially optimal oligotrophic state, a
politician can ensure that he is elected. This shows that political ambition can
indeed prevent socially desirable policy from being implemented.
Appendices
A Phosphorous Sources and Sinks
With the stock of phosphorous held constant, the phosphorous sink and source
equations can each be plotted as in Figure 5 and by Carpenter et al. (1999)
to show the rates of flux of phosphorous against the quantity of available P .
Superimposing the phosphorous sinks’ straight line and the phosphorous recy-
cling’s sigmoid shows the domains of attraction of oligotrophic and eutrophic
states. The upper point of instersection between the two curves is an attrac-
tor toward oligotrophy, whereas the lower intersection is an attractor toward
eutrophy. The intersection point in the middle is an unstable repeller and rep-
resents a Skiba point. This means that at this level of phosphorous stock, a
small change in the stock could precipitate the lake into either an oligotrophic
or eutrophic state. This illustrates the possible existence of a hysteresis in the
lake’s response to phosphorous input.
The graph illustrates that a eutrophied lake can be restored in several ways:
Figure 5: Phosphorous Sources and Sinks
• By increasing the sinks, i.e., by affecting s and thus altering the slope
of the ‘sinks’ line thereby changing the points of intersection with the
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