An indifference curve is a graph that represents all the combinations of two goods that give an individual the same level of utility, or satisfaction. An individual's preferences are represented by the slope of the curve, which shows the rate at which the individual is willing to trade one good for another.
One important property of indifference curves is that they cannot intersect. This is because if two indifference curves intersect, it would mean that an individual is indifferent between two different sets of goods, which is a contradiction.
To understand why two indifference curves cannot intersect, consider the following example:
Suppose an individual has two indifference curves, IC1 and IC2, which intersect at point A on a graph with goods X and Y on the x-axis and y-axis, respectively. At point A, the individual is equally satisfied with receiving goods X and Y in any combination. However, this means that the individual is also equally satisfied with receiving more of either good.
For example, if the individual receives more of good X at point B, which is above and to the right of point A, they would be equally satisfied with receiving more of good Y at point C, which is above and to the left of point A. This means that the individual would be indifferent between receiving goods X and Y in any combination, which is a contradiction.
Therefore, it is impossible for two indifference curves to intersect because it would mean that an individual is indifferent between two different sets of goods, which is not possible. This is why indifference curves are always drawn as non-intersecting curves.
In conclusion, two indifference curves cannot intersect because it would mean that an individual is indifferent between two different sets of goods, which is a contradiction. This is an important property of indifference curves that helps economists and other social scientists understand how individuals make choices and trade-offs between different goods.
