Marginal utility ($u^{\prime }(x)$)

The additional utility function obtained per additional unit of consumption or portfolio wealth. For a differentiable utility function it is its derivative; for a concave utility function it is nonincreasing. In a complete-market allocation, equating marginal utility to a multiplier times the state-price density compares the utility benefit of a payoff with its financing cost. The concave supporting-tangent inequality makes this comparison a global optimality certificate rather than only a local first-order condition.