Think at the margin, but why? (2)

   Economists think at the margin. But how to justify this way of thinking? I find many justifications not obviously persuasive to me. Hence, I have written a post to express my reservation, and offer my own answer to explain why we should think at the margin. 

   Having done this, I remember that Gregory Mankiw's popular textbook Principles of Economics has listed out ten important principles of economics (in Chapter 1), and the third one is "rational people think at the margin". I read it and find some new arguments or examples to support the principle. On the whole, Mankiw did give better examples/arguments than what my past post has used (from another book). But I still have problems. 

   Anyway, let me first share with you what I think are better examples. 

1. Phone call. "[S]uppose you are considering calling a friend on your cell phone ....talking with her for 10 minutes would give you a benefit...at about $7. Your cell phone service costs you $40 per month plus $0.50 per minute.... You usually talk for 100 minutes a month, so your total monthly bill is $90. ... You might be tempted to reason as follows: 'Because I pay $90 for 100 minutes of calling each month, the average minute on the phone costs me $0.90. So a 10-minute call costs $9. Because that $9 cost is greater than the $7 benefit, I am going to skip the call.' That conclusion is wrong, however. Although the average cost of a 10-minute call is $9, the marginal cost—the amount your bill increases if you make the extra call—is only $5....Because the marginal benefit of $7 is greater than the marginal cost of $5, you should make the call."
2. Airline ticket. "Consider an airline deciding how much to charge passengers who fly standby. Suppose that flying a 200-seat plane across the United States costs the airline $100,000. ...the average cost of each seat... is $500. ...Imagine that a plane is about to take off with 10 empty seats and a standby passenger waiting at the gate is willing to pay $300 for a seat. ...If the plane has empty seats, the cost of adding one more passenger is tiny. The average cost of flying a passenger is $500, but the marginal cost is merely the cost of the can of soda that the extra passenger will consume. As long as the standby passenger pays more than the marginal cost, selling the ticket is profitable."

   In my past post, I use an example given by another book: one should not drink one more coke with a marginal benefit lower than marginal cost although the average benefit of this coke is still higher than the average cost. I argue that this example involves a sequential decision: after I drink one coke, I am considering should I drink one more. In the real world, sequence in decision is often not involved. If so, thinking at the margin may not be obviously necessary. 

   Nevertheless, in Mankiw's examples, thinking at the margin is necessary. Failure to do so will lead to fallacies. The reason why is that, in both examples, fixed cost (sunk cost indeed) is involved. The $40 monthly cost of telephone service is fixed regardless of how many minutes of calls are made. The $40 has also been paid and will never be refunded. Thus, you should not consider this $40 when receiving calls. Only the marginal cost of receiving an extra call is relevant. Similarly, $100,000 is a fixed cost of running a flight. With or without extra passengers, this $100,000 is not changed, has been paid (once the plane takes off), and will not be recovered. Hence, this fixed and sunk cost should not be considered when deciding to add one more passenger or not. 

   Arguably, these problems also involve a decision sequence. The first step is to consider paying the $40 or not, and flying or not (thus incurring $100,000). The next step is to consider receiving a call or not, and adding one more passenger or not. The next-step decision should be sort out by thinking at the margin. The sequence is generated because of fixed and sunk cost. Such cost is present in many real-world situations. So, thinking at the margin is relevant. Mankiw's examples are better as he leads us to a context where decision in sequence is relevant. 

   However, when we say firms should produce at where MR=MC, there is no actual sequence involved. The firm will not stop the machine and decide if one more product should be produced. The sequence, at best, exists only in the firm owner's mind. The owner can sort out from the very beginning by comparing different production plans with different outputs. He or she should choose the plan that gives rise to the highest total profit. Thinking in the total is equally effective and is perhaps a more intuitive way of thinking. 

   Mankiw has also given another illuminating example -- the paradox of diamond and water -- to illustrate the important of thinking at margin. 

   "Why is water so cheap, while diamonds are so expensive? Humans need water to survive, while diamonds are unnecessary.  Yet people are willing to pay much more for a diamond than for a cup of water. The reason is that a person’s willingness to pay for a good is based on the marginal benefit that an extra unit of the good would yield. The marginal benefit, in turn, depends on how many units a person already has. Water is essential, but the marginal benefit of an extra cup is small because water is plentiful. By contrast, no one needs diamonds to survive, but because diamonds are so rare, people consider the marginal benefit of an extra diamond to be large."

   This is of course a right example. But it reveals a completely different type of reasons why one should think at the margin. 

   For the phone call/airline example, not to think at the margin leads to unwise decision -- you haven't done what's best for you. For the diamond/water example, it has nothing to do with wrong decision. It is an explanation of why something happens -- diamond is expensive while water is cheap. 

   In fact, there is an ambiguity involved in the term "margin" in this example. Does it mean the last unit or an additional unit? Water is cheap because the last unit of it is not very valuable, provided that we have had plenty already. But one more unit of water may be very valuable if we are very thirsty, without already consuming a plenty of it. 

   Hence, you may imagine that if water was supplied by a monopolist and the monopolist might price-discriminate -- for the initial units you buy, it charges you a high price; for the subsequent units you buy, it charges you a lower price. Then, not only the "last unit" (marginal unit) matters to the price of water, the units before the last unit also matter (prices are different at different marginal units). When we are taught to "think at the margin", which margin (last or additional) we are talking about? What attitude we should have (to ensure we make the best decision or to understand what happens)? 

   I do not intend to criticize Mankiw in this post. As you have seen, I basically appreciate his better example. However, I think we must think more about the principle of "think at the margin". 

   My point is, "think at the margin" is certainly an important principle in economics. But we must be aware what this principle is really about and why this principle is useful. This principle may be ambiguous in some cases and we have to figure out what it means before embracing it. Also, instead of sticking to the principle , "understanding why" is more important. The principle of thinking that is truly important in economics is: understanding the definitions and understanding why. It is not simply to think at the margin.