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Suppose the government wants to determine the efficient price of a certain commodity for which there is no competitive market. One way to do this is to take a sample of the potential buyers and ask them how much they are willing to pay, take a sample of the potential producers and ask them what their costs are, calculate an optimal price on the sample and use it as an approximation to the real price.

I am interested in references about this and similar problems. Particularly, my goal is to calculate bounds on the error of approximation. This seems like a fairly standard question in statistical economics, but I could not find references.

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