Editing Indifference curve (section)

== Map and properties ==
[[Image:Indifference curve example.png|thumb|240px|right|An example of how indifference curves are obtained as the [[level curves]] of a utility function]]
A graph of indifference curves for several utility levels of an individual consumer is called an '''indifference map'''. Points yielding different utility levels are each associated with distinct indifference curves and these indifference curves on the indifference map are like contour lines on a topographical graph. Each point on the curve represents the same elevation. If you move "off" an indifference curve traveling in a northeast direction (assuming positive [[marginal utility]] for the goods) you are essentially climbing a mound of utility. The higher you go the greater the level of utility. The non-satiation requirement means that you will never reach the "top," or a "[[bliss point (economics)|bliss point]]," a consumption bundle that is preferred to all others.

Indifference curves are typically{{vague|reason=Give a few citations of authors who share these requirements; give some notes and citations on authors with deviating requirements.|date=December 2015}} represented{{clarify|reason=Should probably be 'required'.|date=December 2015}} to be:
# Defined only in the non-negative [[Cartesian coordinate system|quadrant]] of commodity quantities (i.e. the possibility of having negative quantities of any good is ignored).
# Negatively sloped. That is, as the consumption of one good increases, to maintain constant utility, a lesser quantity of the other good just be consumed. This is equivalent to assuming [[Local nonsatiation|Local non-satiation]] (an increase in the consumption of either good increases, rather than decreases, total utility). The counterfactual to this assumption is assuming a [[Bliss point (economics)|bliss point]]. If utility ''U = f(x, y)'', ''U'', in the third dimension, does not have a [[Maxima and minima#Functions of more than one variable|local maximum]] for any ''x'' and ''y'' values.) The negative slope of the indifference curve reflects the assumption of the monotonicity of consumer's preferences, which generates monotonically increasing utility functions, and the assumption of non-satiation (marginal utility for all goods is always positive); an upward sloping indifference curve would imply that a consumer is indifferent between a bundle A and another bundle B because they lie on the same indifference curve, even in the case in which the quantity of both goods in bundle B is higher. Because of monotonicity of preferences and non-satiation, a bundle with more of both goods must be preferred to one with less of both, thus the first bundle must yield a higher utility, and lie on a different indifference curve at a higher utility level. The negative slope of the indifference curve implies that the [[marginal rate of substitution]] is always positive;
# [[Total order|Complete]], such that all points on an indifference curve are ranked equally preferred and ranked either more or less preferred than every other point not on the curve. So, with (2), no two curves can intersect (otherwise non-satiation would be violated since the point(s) of intersection would have equal utility).
# [[Transitive relation#Examples|Transitive]] with respect to points on distinct indifference curves. That is, if each point on ''I<sub>2</sub>'' is (strictly) preferred to each point on ''I<sub>1</sub>'', and each point on ''I<sub>3</sub>'' is preferred to each point on ''I<sub>2</sub>'', each point on ''I<sub>3</sub>'' is preferred to each point on ''I<sub>1</sub>''. A negative slope and transitivity exclude indifference curves crossing, since straight lines from the origin on both sides of where they crossed would give opposite and intransitive preference rankings.
# (Strictly) [[convex function|convex]]. [[Convex preferences]] imply that the indifference curves cannot be concave to the origin, i.e. they will either be straight lines or bulge toward the origin of the indifference curve. If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the [[composite good|other good]] are required to keep satisfaction unchanged. Convex preferences are assumed in concordance with the principle of [[declining marginal utility]].