This problem illustrates how marginal analysis might give misleading results in the presence of non-convexity. It is based on an example from Goodstein (1995). Nitrogen oxides (NOx), in combination with some volatile organic compounds and sunlight, can produce damaging lower-atmosphere ozone smog. Initially, the damage rises at an increasing rate with NOx emissions. However, high levels of NOx act as ozone inhibitors, and so beyond some critical level of emissions, higher levels of NOx reduce ozone damage.

(i) Sketch a marginal damage (MD) function that is consistent with these properties.

(ii) Add to your diagram a conventionally shaped marginal benefits function (or marginal abatement cost function) that intersects the MD function in more than one place.

(iii) By an appropriate choice of some initial level of emissions, demonstrate that the following rule may give misleading results.

Rule: emissions should be increased

(decreased) if a small increase in emissions increases (decreases) net benefits.