Your example is interesting and clarifies exchange rates. However,
The shadow price quantifies the opportunity cost, so if I’m paid my shadow price, then that’s just barely enough to cover my opportunity cost.
This is an interpretive point I’d like to focus on. When you move a constraint, in this case with price, the underlying equilibrium of the optimization shifts. From this perspective your usage of the word ‘barely’ stops making sense to me. If you were to ‘overshoot’ you wouldn’t be optimal in the new optimization problem.
At this point I understand that the cheerful price will be equivalent to or more than the shadow price. You want to be able to shift the equilibrium point and have slack left over. It just seems obvious, to me, that shadow price isn’t an exactly measurable thing in this context and so you’d naturally be led to make a confidence interval (belief) for it. Cheerful price is just the upper estimate on that. Hence, I’m surprised why this is being treated as a new / distinct concept.
Your example is interesting and clarifies exchange rates. However,
This is an interpretive point I’d like to focus on. When you move a constraint, in this case with price, the underlying equilibrium of the optimization shifts. From this perspective your usage of the word ‘barely’ stops making sense to me. If you were to ‘overshoot’ you wouldn’t be optimal in the new optimization problem.
At this point I understand that the cheerful price will be equivalent to or more than the shadow price. You want to be able to shift the equilibrium point and have slack left over. It just seems obvious, to me, that shadow price isn’t an exactly measurable thing in this context and so you’d naturally be led to make a confidence interval (belief) for it. Cheerful price is just the upper estimate on that. Hence, I’m surprised why this is being treated as a new / distinct concept.