  Shadow prices are well understood and are widely used in economic
applications. However, there are limits to where shadow prices can be applied
assuming their natural interpretation and the fact that they reflect the first
order optimality conditions (FOC). In this paper, we present a simple ad-hoc
example demonstrating that marginal cost associated with exercising an optimal
control may exceed the respective cost estimated from a ratio of shadow prices.
Moreover, such cost estimation through shadow prices is arbitrary and depends
on a particular (mathematically equivalent) formulation of the optimization
problem. These facts render a ratio of shadow prices irrelevant to estimation
of optimal marginal cost. The provided illustrative optimization problem links
to a similar approach of calculating social cost of carbon (SCC) in the widely
used dynamic integrated model of climate and the economy (DICE).

General Economics;Economics