Postulate of Substitution and Indifference Curve

Chapter 4, Section 4: Postulate of Substitution and Indifference Curve

In the first two chapters of this volume we have said, that to explain behaviors with a theory, the theory must install constraints to the behaviors. That individual maximizes his interest is a constraint, and with the concept of utility, that becomes one maximizes his utility. This constraint is a postulate and doesn't explain too many things. Asserting one maximizes his utility solely is tautology, and with the variation of constraints we can make predictions only when one economic good increases while all the others don't decrease.

The postulate of substitution adds another constraint, and widens the scope of explainable behaviors accordingly. The postulate says: everyone is willing to sacrifice any good he has for any other good. Do you agree or not? Are you willing to sacrifice your life for a bowl of fish ball noodles? This postulate says you are. If only the sacrifice is low enough and the gain is large enough.

When you cross a road to eat fish ball noodles, you are risking your life a little bit — the risk of a car accident is not zero. Like other fathers, I can sacrifice myself for my children — it's love. Yet because of work I don't have much time to stay with them — it's a substitution between love and livelihood.

Don't say that because you are principled, you'd never make a concession on matters of principle. Everyone has his own price, my soul can sell as well. The price is quite high, yet if you offer me a very big benefit while I need give up only a very minor principle, we can make a deal. This is substitution.

Due to everyone is willing to make substitutions, utility analysis thus creates the well know "dengyou quxian", or indifference curve, (normally translated into "wuchayi quxian", or no difference, in Chinese, which is neither elegant nor correct; "dengyou", or equally good, is my translation and gonna become classic). As one is willing to lose A while gaining B, we can find a curve for the two economic goods A and B, on which every point has a same utility. "Indifference" means same utility, and each point is indifferently preferable. Take A as the horizontal axis and B as the vertical, this curve must slope to the lower right, indicating one's indifferent substitution. The curve is a watershed, each point to the upper right of it has a utility higher than any on the curve, while the ones to its lower left go reversely.

Indifference curve enlarges the range of predictions. When there two economic goods, to be more preferable, it doesn't have to be A and B both increase, or A increases while B doesn't decrease: one increases while the other decreases can also be more preferable. There are an infinite number of indifference curves, each two of them don't intersect, and every upper right one has a higher utility number than any to its lower left. Under constraints, a man will choose the highest indifference curve he can reach.