Opportunity cost is what is lost by allocating one's resources to another option. For example, when deciding to spend time sleeping, one loses the opportunity to do something more productive. Opportunity cost can be visually shown by something called the production possibilities frontier. For example, this graph shows all the possibilities that two goods can be produced. Every point on the line would be an efficient use of resources, and point "E" would be an inefficient allocation of resources while point "F" would be unattainable due to a constraint of inputs.  The law of increasing costs states, "To produce more of one good, a supplier must sacrifice increasing amounts of another good." So for a supplier to produce more of good "A" they will be giving up the opportunity to produce more of good "B"

Comparative advantage is denoted by the actor with the lower opportunity cost to produce a product. Before being able to understand the concept of comparative advantage, one must first understand how to calculate opportunity cost. Opportunity cost is calculated by "Change in good X production divided by change in good Y production". It is usually beneficial for countries to trade as it allows countries to produce at not possible prior. 

For example, looking at this hypothetical example table, we can first calculate the opportunity cost of a nail in country A is 1 lightbulb whereas the opportunity cost for nails in country B is 2 lightbulb. Thus, it would make sense for country A to specialize in producing nails as its opportunity cost is lower. Regarding lightbulbs, the opportunity cost for country A is 1 while it is 1/2 for country B. Thus, Country B should specialize in making lightbulbs. Notice that even though country A has the absolute advantage, creating more of a product at a lower cost, in both sectors, it still benefits from trade because of comparative advantage. 

This graph shows that country A will be producing at point 1 while country B will be producing at point 2 considering they specialize. The trading price should be something below the opportunity cost of both countries. Thus, country A would sell nails at more than 3/4 while country B would buy nails at less than 2 nails. So, a possible price would be anything between 3/4-2. Considering that at the trading price of 1, country B trades 15 lightbulbs for 15 nails, country B would now be producing at point 3 and country A at point 4. Both of these points would have been unachievable before so both countries benefit from trade.