Verification of Feasible Frontier Properties using Differentiation
The geometric properties of the feasible frontier, specifically its downward slope and concavity, can be rigorously verified using calculus. The frontier is confirmed to be downward-sloping if its first derivative with respect to free time is negative. Furthermore, its curvature is determined by differentiating a second time. A negative second derivative with respect to free time proves that the frontier is strictly concave, a feature that typically reflects diminishing marginal returns.
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