I already read and ask NOT about pp 52-54, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw. I understand such numerical examples that corroborate Comparative Advantage, but how can I intuit comparative advantage? I wish to quash my need to revisit these numerical examples to recollect this idea. i start with definitions from pp 52 and 53 (supra):

absolute advantage = the ability to produce a good using fewer inputs than another producer

comparative advantage = the ability to produce a good at a lower opportunity cost than another producer

I read this by Prof Steven M. Suranovic and understand the gardening example, but still lack intuition.

First, ... comparative advantage is clearly counter-intuitive. ... Secondly, the theory is easy to confuse with ... the theory of absolute advantage. The logic behind absolute advantage IS quite intuitive. This confusion between these two concepts leads many people to think that they understand comparative advantage when in fact, what they understand is absolute advantage.

However, instead of assuming, as Adam Smith did, that England is more productive in producing one good and Portugal is more productive in the other; [David] Ricardo assumed that Portugal was more productive in both goods. Based on Smith's intuition, then, it would seem that trade could not be advantageous, at least for England.

A classic example is to consider the question

Why doesn't Tiger Woods mow his own lawn?

Woods is an excellent golf player. But he also may be excellent at mowing. Still, if he devotes time to mow the lawn he sacrifices time playing golf, in which he is much more productive.

A gardener who is skilled at mowing lawns but not at playing golf sacrifices less in order to mow, so even though Tiger Woods may be better at it (i.e. has an absolute advantage), the gardener has a comparative advantage. Both benefit if the gardener is paid for the time that he mows the lawn by Tiger Woods who in the time he saves can earn more by concentrating on golf.

1. You have, at least, 2 players. (To be able to compare them).
2. You have, at least, 2 goods, Q1 and Q2. (If you have only one you can make a conclusion only about absolute advantage.) Each player is capable to produce both goods.

Intuition A. To understand absolute advantage, note that both players have the same amount of resources. This fact usually is not that visible and should be thought of thoroughly. Suppose that both players produce only one of goods. A player that can produce more has an absolute advantage. She simply can do more from the same resource, meaning that her average costs are lower (Average costs = fixed_resources / quantity; so the larger the quantity, the less the costs). This is applicable to both goods. So we define max(Q1) and max(Q2) - corner solutions meaning that all resources are spent on Q1 or Q2 respectively.

Intuition C. Comparative advantages are based on marginal costs, not average. That is why they are not intuitive (people cognitively have problems with marginal calculations). To ease comprehension, many textbooks use linear models. In a linear model (in goods Q1-Q2 space, where Q1 - horizontal) slope of a production possibilities curve reflects opportunity costs: only in this case -dQ2/dQ1 = max(Q2)/max(Q1). So, opportunity costs are real costs of Q1 in terms of Q2. In other words, it looks like we pay in Q2 units for a unit of Q1. The player that has a lower slope - less opportunity costs - has a comparative advantage. Put it differently, the player that pays (or 'sacrifice') less Q2 for a unit of Q1 has comparative advantage in Q1. That's it.

Let's look at two companies capable of producing gemstones.

Company A has machinery that produces quartz gemstones which it can sell at \$100/stone. It costs$10/stone in raw materials and \$20/stone in operating costs to produce the stones. Company B has uses different machinery, but also produces quartz gemstones with identical \$100/stone sales and identical \$10 + \$20 cost structure per stone.

So the companies have the same absolute competitive advantage.

However, Company B's machines are more flexible, and can be used to produce diamonds instead of quartz. Here, the diamonds sell for \$10,000/stone and cost a total of \$1,000 in cost to make. Company A's machines are specialized so they can only be used to produce quartz or cheaper and less profitable gemstones.

Company B is much better off producing diamonds than quarts. So the opportunity cost of producing quartz is very high for that Company. By contrast, Company A's opportunity cost is very low.

So Company A has a comparative competitive advantage over Company B, both by definition and also, hopefully, by intuition.