Quasilinear utility

In other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope.

In two dimensional case, the indifference curves are parallel; which is useful because the entire utility function can be determined from a single indifference curve.

then, maximizing utility subject to the constraint that the demands for the two goods sum to a given income level, the demand for y is derived from the equation