The law of increasing opportunity costs says that, as we produce more of a particular good, the opportunity cost of producing that good increases. The main reason for this is the fact that not all resources are created equal. Some resources are better than others for producing certain goods (or services).
Let us imagine an example where I am a farmer and I grow wheat and chickpeas on my land. For the purposes of our example, let us say that some of my land is better for growing wheat, some is better for growing chickpeas, and some is equally good for both. Right now, I have wheat planted on the land that is best for wheat and chickpeas on all the rest of the land. At this point, the opportunity cost of raising the wheat is very low because the land I am using would not grow many chickpeas. Now let us imagine that I have decided to grow more wheat.
As I start to grow more wheat, I will need to use some of the land that is equally good for growing both crops. This means that my opportunity cost for growing the wheat is rising because I am using land that can grow more chickpeas than the land that is best for wheat. Now imagine I decide to grow even more chickpeas. I start to use the land that is really good for chickpeas and not good at all for wheat. As I do this, I am giving up a lot of potential chickpea production in order to grow more wheat. This is an example of the law of increasing opportunity costs.
Because not all resources are equally useful for producing all things, we tend to encounter rising opportunity costs as we increase production of a particular good.
Please follow the link below for a longer discussion of this topic, including a table that illustrates this law in numerical form.