Indifference curves are incapable of intersecting with one another because, by definition, each curve show combinations of different goods that give consumers equal levels of utility. Different curves are drawn for different utility levels and consequently do not intersect.
Indifference curves are used in microeconomic theory to represent graphically the different bundles of goods between which a consumer is indifferent. Indifference refers to the lack of consumer preference for one bundle over another. Different points on a single indifference curve represent equal levels of utility, an ability to satisfy customer need or want. Utility can be quantified and used to denote consumer preference without indicating how this preference arose. Indifference curves are used to represent potentially observable demand patterns for consumers over different commodity bundles in product and service industries.
Indifference curves were first developed by economists Francis Ysidro Edgeworth and Vilfredo Pareto in the early 20th century. The theory behind indifference curves is derived from ordinal utility theory, which hypothesizes that consumers always rank consumption bundles in order of personal preference. The theory assumes that individuals are rational, having internally consistent sets of preferences that do not change during the time-frame needed to analyze their behavior and deduce the curves.