The concept of elasticity is defined as the percentage

The convex shape of the production possibility boundary is derived from the principle of opportunity cost. The production possibility boundary defines the maximum production potential of an economy given its resource and technology constraints.The opportunity cost is defined as loss of economic value that could have been gained if resources had been invested in an alternative. Therefore, the opportunity cost is an integral component of the production possibility boundary in terms of how much of one product can be produced given its opportunity cost.The convex shape of the production possibility boundary means that as the economy produces more of one good, its opportunity cost rises. As a result, fewer quantities of that good can be produced. In other words, more of the other good have to be sacrificed.This is because, as a result of being driven by resource and technology constraints, the economy is in the optimum position of producing a certain quantity of each category of goods. Be yond that point, the opportunity cost of producing one good instead of another continues to rise as it requires increasing resource and technology investments.