Final answer:
Modeling production as convex aligns with real-world observations of diminishing marginal returns and economies of scale. It demonstrates the adaptiveness of firm's production choices in response to cost and input substitution, which is why a production possibilities frontier is typically convex (curved).
Step-by-step explanation:
Modeling production as convex in inputs makes sense in the real world because it reflects the concept of diminishing marginal returns and the necessity for firms to optimize production based on resource availability and cost. The production possibilities frontier (PPF) is typically drawn as a curve to represent these economic realities. When firms transfer resources from the production of one good to another, there is a comparative advantage until a point is reached where producing more of one good greatly increases the opportunity cost.
Additionally, the concept of economies of scale is illustrated since as the quantity of output increases, the cost per unit decreases. This demonstrates that production efficiency increases with scale, allowing firms to lower the average cost of production. Firms modify their input use based on resource prices, favoring less expensive inputs over more costly ones, and the PPF curve reflects this adaptive behavior.