The Wikipedia page is not exactly easy to read for someone not already familiar with the term. My impression (possibly wrong) is that “shadow price” = estimate of a hypothetical market price, if the thing is actually not on the market (therefore it is impossible to look at the actual price).
So, first, there is a difference in usage. “Shadow price” is used in context of buying something for money, or producing it (which would cost you money and other resources). “Cheerful price” is used in context of selling, typically your work and time. In other words, you estimate “shadow price” of things you want, and “cheerful price” of things someone else wants you to do.
Second, there is a difference in precision. “Shadow price” tries to be as accurate as possible (in a situation where it is difficult to be accurate). “Cheerful price” tries to be safe. That is, if your probability distribution is like: most likely $200, but there is a small chance it is $100 or $300, you would choose $200 for the “shadow price”, but $300 for the “cheerful price”.
The Wikipedia page is not exactly easy to read for someone not already familiar with the term. My impression (possibly wrong) is that “shadow price” = estimate of a hypothetical market price, if the thing is actually not on the market (therefore it is impossible to look at the actual price).
So, first, there is a difference in usage. “Shadow price” is used in context of buying something for money, or producing it (which would cost you money and other resources). “Cheerful price” is used in context of selling, typically your work and time. In other words, you estimate “shadow price” of things you want, and “cheerful price” of things someone else wants you to do.
Second, there is a difference in precision. “Shadow price” tries to be as accurate as possible (in a situation where it is difficult to be accurate). “Cheerful price” tries to be safe. That is, if your probability distribution is like: most likely $200, but there is a small chance it is $100 or $300, you would choose $200 for the “shadow price”, but $300 for the “cheerful price”.