This gives us a clear interpretation of the Lagrange multiplier in the context of consumer maximization. If the consumer is given an extra unit of income (the budget constraint is relaxed) at the optimal consumption level where the marginal utility per unit of income for each good is equal to formula_8 as above, then the change in maximal utility per unit of additional income will be equal to formula_8 since at the optimum the consumer gets the same amount of marginal utility per unit of income from spending his additional income on either good.