Derivation of Production Possibility Frontier

Imagine two farmers—one growing oranges and the other growing apples—sharing a fixed amount of labor and capital. 

In an Edgeworth Box, the contract curve represents all efficient input allocations between the two farmers. 

Now, let’s connect this to production. Each efficient input allocation in the Edgeworth Box leads to a specific combination of apples and oranges that can be produced. 

When we map these output combinations onto a graph, we get the Production Possibility Frontier (PPF). This curve connects all possible efficient output combinations of two goods, given the available resources and technology.

Points on the PPF represent efficient production levels where resources are fully utilized. However, if resources are misallocated or underutilized, production falls inside the PPF, as represented at point F. To move from F to G, the farmers must improve efficiency.

Additionally, the PPF slopes downwards because producing more apples requires sacrificing some oranges, and vice versa. The slope of the PPF, known as the Marginal Rate of Transformation, quantifies this trade-off.