Figure 2-8 Non-linear Pollution Reduction
must be spent in order to reduce pollution by 1000 tonnes. At that point,
each tonne of pollution reduction therefore costs $6.
Pollution as a non-linear function of clean-up expenditure. The slope of
the curve changes as we move along it. Between points A and B, it costs
$1000 to reduce pollution by 1000 tonnes. Between points C and D, it
costs $6000 to reduce pollution by 1000 tonnes. At point Z, the slope of
the curve is equal to the slope of the straight line tangent to the curve at
point Z. The slope of the tangent line is
Economists call the change in pollution when a bit more or a bit less is
spent on clean-up the marginal change. The figure shows that the slope of
the curve at each point measures this marginal change. It also shows that
in the type of curve illustrated, the marginal change per dollar spent is
diminishing as we spend more on pollution reduction. There is always a
payoff to more expenditure over the range shown in the figure, but the
payoff diminishes as more is spent. This relation can be described as
−0.75/1.75=−0.43.