One of the basis of economics is the idea that resources are scarce, and insufficient to satisfy all the needs of mankind. With limited resources, a company can only produce a limited amount of products. Therefore, there is a limit in the capacity of production, graphed by the production possibilities frontier curve. Changes in some factors, like technological advances, lower cost of labor and many other factors can shift the curve to the right, increasing the the limit of production. Consider Company ABC, which produces two products: product A and product B. Splitting all of ABC's resources in half (for each product), ABC produces 100 units of A and 50 units of B.
The production possibilities frontier always shows two products, X and Y. The curve assumes the maximum productivity possible (maximum number of people working, maximum efficiency, applying the latest technology and other factors), and shows the quantities created of each product. If the company ABC would like to increase the quantity of product A, the only way to do it is to take resources used in the creation of product B and use them to create more of product A. This causes the company to create more A, but less B. This choice for resources allocation is represented on the convex shape of the curve.
The opportunity cost is another reason for the production possibilities frontier. Opportunity cost is the concept of expressing the cost of producing product X in terms of the quantity of product Y that has not been produced. Company ABC chooses to increase the production of A from 100 to 150 units. Since the company is already working at maximum efficiency, this increase in A will cause a decrease from 50 units of B to only 25 units. In other words, to produce 50 more units of A, ABC sacrificed 25 units of B. This is called the opportunity cost of A.
Since each company is different, their production possibilities frontiers are different as well. The difference in these curves also causes different opportunity costs. From the example, ABC produced 100 units of A and 50 of B. XYZ, a second company, produces 20 units of A, and 20 units of B. The opportunity cost of ABC to produce A is to sacrifice one unit of B for two units of A. The opportunity cost of XYZ to produce A is to sacrifice one unit of B for one unit of A. Since XYZ's opportunity cost to produce A is lower, it should specialize in producing B, and ABC should specialize in producing A.
Before:
ABC: 100 A, 50 B
XYZ: 20 A, 20 B
Total output: 190 units
After specialization:
ABC: 200 A, 0 B
XYZ: 0 A, 40 B
Total output: 240 units
When companies (or countries) specialize, they increase the total production output.