The indifference curve through formula_56 must deliver at each bundle on the curve the same utility level as bundle formula_56. That is, when preferences are represented by a utility function, the indifference curves are the level curves of the utility function. Therefore, if one is to change the quantity of formula_66 by formula_67, without moving off the indifference curve, one must also change the quantity of formula_68 by an amount formula_69 such that, in the end, there is no change in "U":