14.15 : Derivation of Production Possibility Frontier

The Edgeworth Box illustrates all possible ways to allocate a fixed amount of labor and capital between two firms—one producing wheat and the other producing cotton. Each point within the box represents a specific allocation of these inputs between the two firms. Among these points, the contract curve highlights all Pareto-efficient allocations, where no reallocation of labor or capital can increase one firm’s output without reducing the other’s. This condition defines Pareto efficiency, the point where inputs are shared in a way that fully utilizes their potential for both firms.

Each efficient input allocation along the contract curve generates a particular combination of wheat and cotton output. By plotting all these output pairs, economists derive the Production Possibility Frontier (PPF). The PPF represents the maximum combinations of wheat and cotton that the economy can produce if resources are allocated efficiently. The PPF typically appears concave, reflecting the principle of diminishing returns—as more inputs shift toward wheat production, those inputs become less effective because they are better suited for cotton. This declining productivity results in a rising opportunity cost, meaning the economy must sacrifice increasing amounts of cotton to produce each additional unit of wheat.

Every point on the PPF reflects efficient production, where all resources are fully and productively employed. In contrast, any point inside the PPF signals inefficiency. Such inefficiency may stem from underutilization of labor or capital, misallocation of inputs, or deeper causes such as structural rigidities or institutional constraints—for instance, outdated regulations, weak infrastructure, or technological limitations.

Over time, the PPF can shift outward if the economy acquires more resources or improves technology. This outward shift reflects long-run economic growth, allowing the economy to achieve higher production levels across both goods.