The Science of Demand (24) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 4.  The Substitution Postulate and the Indifference Curve

In the first two chapters of this Volume, we have said that in order to apply theory to explain behavior, behavior must be restrained by theory. The restraint of constrained maximization, when combined with the utility concept, becomes maximization of utility number. This restraint is a postulate, though cannot explain much of human behavior. It is a tautological statement saying that whatever one does is to maximize utility number. When changes in constraints are asserted, what we can infer is only limited to choices like an increase in one economic good without concurrent reduction of other goods.

When restraints are supplemented by the postulate of substitution, the scope in explaining behavior is enlarged. This postulate says: every individual is willing to give up whatever good to exchange for whatever other good. Agree? Are you willing to sacrifice your life to exchange for a bowl of fish-ball noodles? This postulate says that you are willing, as long as you get back more than you give up.

Crossing the road to have a bowl of fish-ball noodles bears a little bit of risk to your life, since the risk of traffic accident is higher than zero. Like other fathers, I am willing to sacrifice a lot for my children – this is love. Yet in order to work, I have not spent much time with my children – this is the substitution of livelihood for love.

Don’t say that you are a man of high principle that for certain matter of principle, you will never give in. There is a price for everything, every person included. For a reasonably high price, my soul can be sold. If lucrative “gains” can be obtained at the expense of giving up negligible principle, I would “transact” with you. This is substitution.

Since everyone is prepared to exchange, the utility analysis has created the renowned “indifference curve”. Since we are willing to exchange A for B, two economic goods, it is very easy to find a curve between A and B so that the utility number thereon remains the same. “Indifference” refers to having the same utility number on every point of the curve, i.e., every point is equally preferred. With A as the vertical axis and B the horizontal axis, this curve will definitely slope downward toward the right, representing indifferent substitution to every chooser. This curve therefore becomes a watershed. Every point lying to the right of the curve has a higher utility number than every point on the curve, and is thus preferred. The opposite is true for every point lying to the left of the curve.

The indifference curve has proved useful in restraining behavior. Between two economic goods, to be better off, one’s choice does not have to be more of both A and B, or more of A while B remains unchanged: more of one at the expense of the other may still be better. There are infinite indifference curves with no two of them intersecting. And the utility number of each curve lying on the right is definitely higher than that of the curve on the left. Under constraints, one will choose the indifference curve with the highest utility number.