The law of demand, but why?

   I have recently met with a first-year student who has a fresh knowledge of high-school economics, and has not yet been affected by university teaching of economics (as the semester has just begun). He got 5** (the highest grade) in economics from DSE, the Hong Kong's high-school public exam. He can also answer questions in exactly the same way as what the textbook brought by him says. Hence, I trust what he says is what is taught in DSE economics.
   To my surprise, I have learned from him that, in the DSE syllabus, there is no explanation given for why the demand curve of an individual good is downward-sloping. It simply says that this is the law of demand. By contrast, why aggregate demand curve is downward-sloping will be explained as required by the syllabus.
   I do not think we should avoid explaining why demand curve is downward-sloping in microeconomics in high school. We may not need a complicated or technical explanation at high-school level. But we had better give some intuitive reasons. Furthermore, not explaining it in micro but explaining it in macro, to me, is odd.
   The law of demand is a very important part in basic economics. If no explanation is given for this law, the syllabus misses something very important. Economics is a social science, and one primary task of science is to explain what happens. If you ask me simply to believe in something that is true, I will be very frustrated and doubt whether this is what a scientist normally would do. Of course, if we cannot explain something, honestly admitting this is still what a scientist should do. But obviously economics can explain the law of demand.
   Perhaps one could argue further in this way: Science does not explain everything. At some point, you must accept that something are unexplained. If something must be unexplained, perhaps we can also choose which is to be explained and which is not to be explained (like what a mathematician chooses axioms). We can choose not to explain the law of demand but use the law as a basis to explain everything else.
   I am not sure if this is the reason behind the DSE syllabus. If so, I think this is also not a good way to handle (delete) the explanation of the law of demand. First, I am not aware of anywhere else that will adopt this justification in designing high-school syllabus, especially this involves a rather non-straightforward methodological viewpoint. Second, though I know there may be a few economists holding a similar methodological viewpoint, this is not a viewpoint that most other economists in the world hold. Obviously, the global viewpoint (reflected in tremendous amount of textbooks) is that the law of demand can be explained and has been explained. I see no reason why a barely accepted methodological viewpoint should be accepted for designing high-school syllabus.
   Given all these, I must say I do not think DSE should avoid explaining the law of demand.
   Furthermore, if DSE syllabus designers think that aggregate demand can be explained at the high school level, they should also think that demand curve in micro can be explained. It is not more difficult to explain the micro demand curve. I will touch on aggregate demand later by writing another post. At the moment, I simply want to emphasize that explaining the law of demand never involves complicated highbrow technique, and there is already a standard answer, a universally accepted answer in university textbooks. What teachers need is only to explain the two reasons behind in intuitive terms (not in technical terms as in university textbook): substitution effect and income effect.
   The idea is in fact quite intuitive. Any conscious consumer will buy goods with a goal to achieve (e.g. attaining certain level of satisfaction from consumption) and with a constraint restricting her choice (e.g. a fixed income for use in a period). If the price of a good (e.g. apple) falls (say, from $5 each to $4 each), other things (e.g. orange price at $5, income at $100) being equal, then one can spend less ($90 instead of $100) and can still buy the same basket of goods as before (e.g. 10 applies and 10 oranges a month). Given the same income ($100) as before, there is some money unspent ($10), and can be used for buying extra goods. Hence, although the consumer's income is unchanged (at $100), the consumer still has extra money ($10) for use (even if she buys the same basket of goods as before). The situation is equivalent to an increase in the consumer's income (by $10). Though her income is unchanged, the purchasing power of her income increases (when price of a good falls). This is the so called income effect.
   How will income effect affect the quantity purchased? Normally, when income increases, individuals buy more goods. Thus, we expect she buys more apples due to the income effect (i.e. due to the extra money she can use even after buying the same basket of goods as before).
   Meanwhile, a lower price of a good (apple) also generates a substitution effect. As we have mentioned, a conscious consumer buys goods with a goal to achieve. Different goods may help her achieve the same goal in a different manner. In this sense, goods are substitutes. For example, both apple and orange enables one to absorb similar nutrients. Though they are not perfect substitutes, and one apple is not exactly equivalent to one orange, they can be replaced by each other to a certain extent. People want to achieve the same goal at lowest cost. Thus, when apple price falls, a consumer will tend to replace (some) oranges by (some) apples. Doing so enables her to achieve her goal at a lower cost.
   In other words, both income effect and substitution effect support the law of demand: when the price of a good falls, the quantity demanded of the good increases. The reason is as simple as this. When students move on to study economics in university, they can be taught the same reasons (substitution effect and income effect) using technical terms (e.g. utility) and with some variants or exceptions (e.g. Giffen goods). The case will become not very simple at that time but these need not be the concern of high schools. However, at the high-school level, the easier version (without technical terms) of the explanation should be understandable to students, and should not be avoided.