Individual welfare is most naturally measured in terms of individual utility but this has the well-known disadvantage that utility levels of different consumers cannot be meaningfully compared. This difficulty is traditionally avoided by using various willingness-to-pay measures, such as...

The method of steepest descent for solving unconstrained minimization problems is well understood. It is known, for instance, that when applied to a smooth objective function f, and converging to a solution point x where the corresponding Hessian matrix F(x) is positive definite, the asymptotic...