More on "The law of demand, but why?"

   My earlier post "The law of demand, but why?" is one of my most widely read post in this blog. On one hand, this is perhaps due to its being related to high-school economics education, which can more easily arouse students' attention. On the other hand, this is perhaps due to its really touching on some important points.
   Two (very smart) students asked me questions over the reason why demand curve is downward sloping upon reading my blog post. They raised some similar points. Let me share with you the question and my response here.
   One student said that he has learned the concept of marginal benefit (of consuming a good) although he has not learned substitution effect and income effect as introduced in my post mentioned above. The marginal benefit (MB) is the additional benefit generated by consuming one more unit of a good. MB curve is downward sloping (when one consumes one more good, the extra benefit from this good is smaller). Hence, this is an explanation of why demand curve is downward sloping.
   Is using MB curve sufficient for explaining demand curve? In my view, this is not sufficient. I do not know precisely what the student has learned about MB. Is MB the monetary value or monetary benefit that a consumer can derive from a unit of good? If so, then MB is the same, at least almost the same, as demand curve. Saying that MB is downward sloping is equivalent to say that demand curve is downward sloping. But this is not an explanation of why demand curve is downward sloping.
   If MB is NOT the monetary benefit one can derive from a good but the satisfaction derived from a good, for example, the psychological or physical benefit, then MB is not equivalent to a demand curve. But a downward-sloping MB curve CANNOT be directly translated into a downward-sloping demand curve. The units for MB is satisfaction level; the unit for demand curve is money (price). To translate the MB schedule into a demand schedule, we need something in extra, such as the substitution effect and income effect.
   The above is a relatively simple answer to the question. To answer further, it will involve economics beyond the level required by the readers of "hi, economics" (high school level). So, perhaps I am forced to stop here. Nonetheless, let me simply give you some hints for the thinking. What follows is not a rigorous analysis, which must be too technical for a blog. As I try to make a more intuitive explanation, I guess my explanation below might even be a little bit misleading when evaluated by rigorous logic. However, I hope it can serve to give you some hints.
   Why MB in satisfaction term (or in utility term in economics) is not the same as demand in money term? To make things clearer, let me call MB in satisfaction terms marginal utility (MU). MU of x is not the same as demand curve. We need to divide MU of x by the MU of money (or income) to make things measured in money term (as required by the demand curve). What is MU of money? Well, it is about how many more units of satisfaction (or utility) that can be generated by having one extra unit of money.
   To illustrate, consider a numerical example. Suppose that consuming one extra unit of x gives you 6 extra units of utility while an extra $1 gives you 2 extra units of utility. Then, you are willing to pay a price of (or sacrifice) $3 for getting this extra unit of x.  By this logic, the demand curve should be MU of x divided by MU of money (6/2), not just MU of x (6).
   Now, imagine one extra unit of x is consumed. The demand curve is, as said, about MU of x divided by MU of money. When x increases, MU of x should decline. This is the effect due to the so-called downward-sloping MB (or MU) curve. But things are not that simple. If x increases, one must reduce consumption of another good, say, good y, due to a fixed income. When y decreases, the MU of y will increase (if the MB or MU curve of y is also downward sloping). Furthermore, MU of money (income) should also change when there is a change in consumption portfolio as above. Thus, demand curve is not simply about MB or MU of a good but more factors. These factors include how far goods (x and y) can be substituted for one another (in generating utility) and the effect from income (in generating utility).
   OK, perhaps you think the last three paragraphs are complicated and makes you confused. Well, as you can see in my post "The law of demand, but why?", it is not difficult to understand the reason why demand curve is downward sloping by substitution and income effect. The troubles come only if you try to relate substitution and income effect to MB curve. As MB curve is not as proper a way to explain demand curve, I would suggest that you directly think in terms of substitution and income effect as what my past post does.