Ramsey problem

The Ramsey problem, or Ramsey pricing, or Ramsey–Boiteux pricing, is a second-best policy problem concerning what prices a public monopoly should charge for the various products it sells in order to maximize 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 inverse 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 found this 1927 in the context of Optimal taxation: the more elastic the demand or supply, the smaller the optimal tax.^[1] 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 price equals to marginal cost, so it must set prices for some or all of the products it sells to above marginal cost if it is to be viable without government subsidies. Ramsey pricing says to mark up most the goods with the least elastic (that is, least price-sensitive) demand or supply.