Editing Ramsey problem (section)

{{Short description|Problem of setting prices by a public monopoly}}
The '''Ramsey problem''', or '''Ramsey pricing''', or '''Ramsey–Boiteux pricing''', is a [[theory of the second best|second-best]] policy problem concerning what prices a public [[monopoly]] should charge for the various products it sells in order to maximize [[Welfare economics|social welfare]] (the sum of producer and consumer surplus) while earning enough revenue to cover its fixed costs.

Under Ramsey pricing, the price markup over marginal cost is inversely related to the [[price elasticity of demand]] and the [[Price elasticity of supply]]: the more elastic the product's demand or supply, the smaller the markup. [[Frank P. Ramsey]] discovered this principle in 1927 in the context of [[Optimal tax]]ation: the more elastic the demand or supply, the smaller the optimal tax.<ref>{{Cite journal|last=Ramsey|first=Frank P.|date=1927|title=A Contribution to the Theory of Taxation|journal=The Economic Journal|volume=37|issue=145|pages=47–61|doi=10.2307/2222721|jstor=2222721}}</ref> The rule was later applied by [[Marcel Boiteux]] (1956) to natural monopolies (industries with decreasing average cost). A [[natural monopoly]] earns negative profits if it sets prices equal to marginal cost, so it must set prices for some or all of the products it sells above marginal cost if it is to remain viable without government subsidies. Ramsey pricing indicates that goods with the least elastic (that is, least price-sensitive) demand or supply should receive the highest markup.<ref>{{Cite web |date=2023-11-07 |title=After 90 Years, Mathematicians Finally Solved the Most Notorious Ramsey Problem |url=https://www.popularmechanics.com/science/math/a45755752/notorious-ramsey-problem-solved/ |access-date=2025-03-27 |website=Popular Mechanics |language=en-US}}</ref>