…the curves cannot cross. Higher is higher. At all points, more of both goods should always move you to a higher curve. When curves cross, this will not occur at all points (draw it and see). More importantly, if you cross curves, you lose the whole predictive power of indifference curve analysis.
The unique feature of the indifference curve is that the utility remain constant all through. The different points on the indifference curve are equally satisfying and a consumer does not prefer a certain combination set to the other. It is possible to plot different indifference curves representing different individual on one Cartesian plane. The different curves will poses unique utility and will form a series on none intersecting curves on the plane. The series of non intersecting curves form an indifference map.
On any two-good graph, a consumer has an infinite number of indifferences curves—one for each level of satisfaction. An indifference curve’s slope is the consumer’s marginal rate of substitution (MRS)—the maximum amount of one good the consumer will sacrifice to obtain one more unit of another good. Marginal utility measures the extra satisfaction from consuming one extra unit of the good, and equal to the partial derivative of the utility function with respect to the particular good. The slope of an indifference curve (its MRS) equals the negative of the ratio of the marginal utility from the good on the horizontal axis to the marginal utility from the good on the vertical axis
Because indifference curves represent a consumer's preferences, they have certain properties that reflect those preferences. Here we consider four properties that describe most indifference curves. Property 1: HIgher curves are preferred to lower ones. […] Property 2: Indifference curves are downward sloping. […] Property 3: Indifference curves do not cross. […] Property 4: Indifference curves are bowed inward.
We have good reason to expect the indifference curves for all consumers to have the same basic shape as those shown here: They slope downward, and they become less steep as we travel down and to the right along them.
...the shape of the indifference curve is not a straight line. It is conventional to draw the curve as bowed. This is due to the concept of the diminishing marginal rate of substitution between the two goods. The marginal rate of substitution is the amount of one good (i.e. work) that has to be given up if the consumer is to obtain one extra unit of the other good (leisure). The equation is below - The marginal rate of substitution (MRS) = change in good X / change in good Y
An indifference curve map shows the family of indifference curves. There could be an infinite number of indifference curves that would reflect the level of utility at different combinations of the two goods. Just as a line on a topographical map indicates the different points that are at the same elevation, the different points along an indifference curve, indicate that same level of utility.
...we also need to know how much a consumer wants to spend on each good. That is, we need some information about this consumer's preferences regarding each good. This information is found in an indifference curve. Indifference curves are drawn with two basic ideas in mind: (a) within certain limits, consumers always prefer more of everything to less [...] and (b) it is possible to derive the same satisfaction out of a variety of potential purchase combinations [...] Therefore, by considering one's preferences, we see that consumers make purchasing decisions which depend upon the satisfaction (more formally, the utility) derived from a particular good. Each unit consumed [...] in a given time period yields some sort of satisfaction. When we examine the amount of satisfaction derived from each unit consumed, we are considering something called marginal utility (MU). The slope of the indifference curve may be expressed as a ratio of the marginal utilities associated with each good (MU2/MU1).
An indifference curve represents all combinations of two goods x and y that provide he individual with an equal level of total utility. (A related concept is the martial rate of substitution (MRS): the amount of X that one must be given, to compensate for a loss of good Y, in order to maintain total utility at a constant level.)
An indifference curve is a collection of all commodity bundles which provide the consumer with the same level of utility. The indifference curve is so named because he consumer would be indifferent between choosing any one of those commodity bundles.