consumers, or they may wish to help the poor by putting more weight on their surplus. Moreover, many people will see Ramsey pricing as unfair, especially if they do not understand why it maximizes total surplus. In some contexts, Ramsey pricing is a form of price discrimination because the two products with different elasticities of demand are one physically identical product sold to two different groups of customers, e.g., electricity to residential customers and to commercial customers. Ramsey pricing says to charge whichever group has less elastic demand a higher price in order to maximize overall social welfare. Customers sometimes object to it on that basis, since they care about their own individual welfare, not social welfare. Customers who are charged more may consider unfair, especially they, with less elastic demand, would say they "need" the good more. In such situations regulators may further limit an operator’s ability to adopt Ramsey prices. Formal presentation and solution Consider the problem of a regulator seeking to set prices for a multiproduct monopolist with costs where is the output of good i and is the price. Suppose that the products are sold in separate markets so demands are independent, and demand for good i is with inverse demand function Total revenue is Total welfare is given by The problem is to maximize by choice of the subject to the requirement that profit equal some fixed value . Typically, the fixed value is zero, which is to say that the regulator wants to maximize welfare subject to the constraint that the firm not lose money. The constraint can be stated generally as: This problem may be solved using the Lagrange multiplier technique to yield the optimal output values, and backing out the optimal prices. The first order conditions on are where is a Lagrange multiplier, Ci(q) is the partial derivative of C(q) with respect to qi, evaluated at q, and is the elasticity of demand for good Dividing by and rearranging yields where . That is, the price margin compared to marginal cost for good is again inversely proportional to the elasticity of demand. Note that the Ramsey mark-up is smaller than the ordinary monopoly markup of the Lerner Rule which has , since (the fixed-profit requirement, is non-binding). The Ramsey-price setting monopoly is in a second-best equilibrium, between ordinary monopoly and perfect competition. Ramsey condition An easier way to solve this problem in