As before, we start with the indifference mapping in X₁-X₂ space, where each indifference curve traces out all combinations of the two goods X₁ and X₂ which yield the same level of utility. Given a fixed budget M and goods prices P₁ and P₂ for the goods X₁ and X₂, we can superimpose the budget line, which shows all just-affordable combinations of X₁ and X₂.

We assume a rational consumer chooses the X₁-X₂ combination which maximizes his/her utility subject to this budget constraint. This optimal combination occurs at the unique tangency point between the budget line and the indifference curve representing the highest affordable level of utility. The slope of the budget line is the price ratio P₂/P₁. The slope of the indifference curve is the ratio of marginal utilities MU₂/MU₁.

We derive the Engel Curve (demand with respect to income) for X₁ by varying M while holding both prices P₁ and P₂ constant, and tracing out the utility-maximizing level of X₁ consumed at each level of M. In this animation, as M is increased, the budget line shifts outward in parallel to new tangency points on successively higher indifference curves, indicating successively higher optimal consumption levels of X₁.

In this example, X₁ is a normal good: its income elasticity is greater than zero. In contrast, if X₁ were an inferior good, consumption of it would decline as income increases: an inferior good's income elasticity is less than zero.

Luxury goods are a subset of normal goods with income elasticities greater than +1.