The Science of Demand (25) - Unofficial Translation of Steven Cheung's 经济解释 - 科学说需求

Section 5.  The Convexity Postulate

We can safely assert further restraint on behavior: the indifference curve must be convex (curving toward the lower left corner) in shape. This restraint (indifference curve is neither straight nor concave) is called the “convexity postulate” or “postulate of diminishing marginal rate of substitution”.

Its implication cannot be more apparent. If utility number does not change (on the same indifference curve), the more a person has of A, the less eager is he to exchange B for A. This postulate is failsafe as long as substitution is made on the same indifference curve. However, when the wealth or income of this person increases, he would jump to another indifference curve with a higher utility number, and the intention to substitute at the margin may also change. This is a big conundrum in inferring behavior using the utility analysis, resulting in its theoretical framework losing the most significant restraint on behavior. Discussion of it is deferred.

The convexity postulate can draw a conclusion using the same indifference curve to predict behavior, though its usage is limited. The conclusion is, if the price of a good falls, the quantity demanded of this good on the same indifference curve must increase. Since prices are always relative, a fall in the price of a good means a reduction in the option forgone of other goods. As such, the decrease in the intention to substitute at the margin will lead to an increase in the quantity demanded of the discounted good.

The problems with indifference curves and utility numbers are that they are merely castles in the air conceived by economists. There are no such curves in the real world, therefore we have no way to find out whether a person’s choice will still be lying on the same curve when the price of a good drops. By logical deduction: when prices fall, the real income of a consumer increases, this consumer will consequently jump to a higher indifference curve. At a higher level, however, the intention to substitute at the margin may have changed. So how can we deal with it?