The production possibilities model shows an inverse relationship between the amount of one thing that can be produced and the amount of something else because

The production of one good will reduce the available resources needed to produce the other good. Since resources are limited, the production or goods competes for them.

Explanation:

This concept can be best illustrated by an example:

A country produces apples and tomatoes. Its production possibilities frontier (PPF) is linear and it can produce 100 apples and 200 tomatoes.

The PPF is determined by the opportunity cost of producing either apples or tomatoes. Opportunity cost refers to the extra costs or benefits lost from choosing one activity or investment from another alternative.

In this case, the opportunity cost of producing apples instead of tomatoes = 200 / 100 = 2 tomatoes per apple produced. The opportunity cost of producing tomatoes instead of apples = 100 / 200 = 0.5 apples per tomato produced.

Resources are scarce, that is the basic premise of economics, and we must allocate of resources in the most efficient possible way in order to maximize our benefits. But no one, not even the richest person or the largest corporation can have all the money in the world, or own all the resources, or even buy an extra 10 minutes per day of time.

The concept of PPF is that you have to choose what combination of goods provides the most benefits per dollar (or per apple/tomato in this case) spent.

The production possibility curve is a graphical illustration and tool used for economic analysis. It shows the various combination of goods that can be produced given available resources.

The PPC looks like a bow shape and has an inverse relationship, this is because this is because to produce 1 more of product A you need tp be willing to let go of 1 unit of product B (assuming we can only manufacture 2 products) this concept is known aa Marginal Rate of Transformation.