Ordinal Utility Approach: Indifference Curves

Economists such as J. R. Hicks and R. G. D. Allen questioned whether satisfaction can really be measured in precise cardinal numbers, and developed the ordinal utility approach instead. Under this approach, a consumer does not need to say by how many utils one combination of goods is preferred to another; the consumer only needs to be able to rank combinations as preferred, less preferred, or equally satisfying. This weaker, more realistic assumption is the basis of indifference curve analysis.

An indifference schedule lists different combinations of two commodities, say bread ($X$) and jam ($Y$), each of which gives the consumer exactly the same level of total satisfaction, so the consumer is indifferent between them — happy with any one of them equally. Plotting these combinations on a graph, with $X$ on the horizontal axis and $Y$ on the vertical axis, and joining the points, gives an indifference curve (IC). A whole family of such curves, one for each possible level of satisfaction, is called an indifference map.

Properties of indifference curves:

• Indifference curves slope downward from left to right (negative slope). If a consumer gives up some units of $Y$, more units of $X$ must be given in return to keep total satisfaction unchanged; both goods cannot fall together without reducing satisfaction.
• A higher indifference curve represents a higher level of satisfaction. A curve farther from the origin passes through combinations containing more of both goods (or more of one with no less of the other), which a rational consumer always prefers.
• Indifference curves are convex to the origin. This follows from the principle of diminishing marginal rate of substitution — as a consumer has more of $X$ and less of $Y$, they are willing to give up progressively smaller amounts of $Y$ for each extra unit of $X$.
• Two indifference curves can never intersect. If they did, the point of intersection would imply two different levels of satisfaction for the very same combination of goods, which is a logical contradiction. …