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The well-known fact that money-metric utility functions cannot be concave in consump- tion has led some scholars to argue against its use in applied welfare analysis. We prove two welfare results: that any competitive equilibrium maximizes the sum of money-metric utilities (the First Welfare Theorem); and that the derivative of the sum of money-metric utilities equals seven other local measures of welfare in a general equilibrium setting. The two most interesting of these are a local measure proposed by Radner (1993); and the ‘co- efficient of resource utilization' proposed by Debreu (1951) (the second measured in units of a numeraire good). The tool we use to prove these results is this: any solution to the consumer's problem for the general non-concave money metric representation must satisfy the famous saddlepoint inequalities from concave programming. The only assumptions are that preferences are locally nonsatiated and continuous. In particular they need not even be convex. We also use the saddlepoint to prove new results in comparative statics: for example we substantially generalize the theorems of Chipman (1977) and Quah (2007), and the characterization of the money-metric definition of complementary goods in Samuelson (1974).
