Indifference Curves & The Indifference Map
We now know that points on an indifference curve all offer the same amount of utility, it follows that points above or below a curve must sit on a different indifference curve. When we plot all combinations of goods for varying levels of utility we get multiple indifference curves. This is illustrated below, and the resulting graph is called an indifference map.
Since these curves each represent a given level of utility, it is typical in the standard economics textbooks to see these curves denoted with the letter U.
Note that each curve must always be higher or lower than another curve at all points. In other words, it is not possible for two or more curves to intersect each other. To see why this is the case, consider the graph below.
At point a, with 18 servings of biscuits and 5 servings of cheese, we know from the blue curve that the consumer is indifferent to point b with only 8 servings of biscuits but an increased 13 servings of cheese. Now, if the red curve was also an indifference curve, it would imply that the consumer is indifferent between point b and point c. Clearly this is not possible since it violates our assumption of non-satiation i.e., that more is always better, because point c has more of both goods than point b.
The only way to maintain our underlying assumptions about preferences from a diagrammatic perspective is to draw each curve as being higher or lower than another curve at all points, as illustrated by the 3 curves in the indifference map above.
The Slope of Indifference Curves
The slope of the indifference curve shows the relative tradeoff in the two-good model between biscuits and cheese. As you can see, as we move from left to right along a curve, its slope declines i.e., it gets flatter and flatter. This is a natural consequence of the law of diminishing marginal utility that I will describe in the next section. Before that, it's important to note that the indifference curve slope relates to the concept of the 'marginal rate of substitution'.
The marginal rate of substitution describes the tradeoff relationship between one good and another, and economists use it in a similar way to the marginal rate of transformation (a concept relating to the production possibilities curve). From an illustrative perspective, it is shown as a straight line tangent that touches the indifference curve point at the relevant tradeoff ratio between the two goods.
For further details about this important concept, and how it builds on our model of consumer behavior, see my article at:
Diminishing Marginal Utility
The slope of the indifference curve also indicates another important aspect of these curves, and that is the diminishing marginal utility that a consumer gets from an increased amount of a good. We do assume that utility can rise uniformly if we have enough money to keep moving to a higher curve, but for any given curve its convex shape shows that as we move along it we need an increasing amount of one good to compensate us for giving up a unit of the other good.
In other words, as consumption of one good increases relative to the other, the consumer gains diminishing marginal utility from it. At very high levels of consumption of one good relative to the other, we are prepared to sacrifice a large quantity of it in order to obtain an additional unit of the other good. Maximizing utility is the goal of any consumer, and you can learn more about this on my page about:
Consumer Income and Budget Constraint
If you have read this far you might reasonably be wondering why any consumer doesn't simply optimize their utility by choosing a bundle of goods with infinite quantities of both. The reason for that is because there has been no mention of the price of these goods or the role of money. All consumers, or almost all consumers, do of course face restrictions on their ability to consume as many goods as they would prefer to do if they had no budget constraint.
Since our level of income sets our budget constraint, it needs to be incorporated into our model of preferences in order to build a more complete picture. For full details and graphs on the budget effect on indifference curves, see my article at:
- Marginal Utility
- Revealed Preference
- The Price Consumption Curve
- The Income Consumption Curve
- The Income Effect
- The Substitution Effect