Transformation Functions: Cost, Revenue Functions, Autarky General Equilibrium, Comparative Advantage

Bjarne S. Jensen ()
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Bjarne S. Jensen: University of Southern Denmark (SDU)

Chapter Chapter 23 in The Elements and Dynamic Systems of Economic Growth and Trade Models, 2025, pp 697-765 from Springer

Abstract: Abstract Reviewing transformation functions, production possibility curves, and factor contract curves, we present explicit formulas of the Transformation Functions for Pareto efficient factor allocations. These production possibility frontiers (Envelopes) are explicitly stated for any Cobb-Douglas (CD) sector technology parameters and any factor endowments of labor and capital. Exact Variable Elasticity of Transformation (VET) curves of non-joint productions are derived. Core Theorems of international trade are unified, extended, and economically stated explicitly with structural parameter formulas. Multiple output Revenue functions are obtained in closed forms. The output formulas of the Transformation and Revenue functions are compared with the autarky general equilibrium expressions. Explicit autarky formulas of comparative advantage (price, cost) for prediction of trade pattern are derived and demonstrated for bilateral trading economies with any CD sector technologies, CD consumer preferences, and any country endowment ratios (proportions) of labor and capital.

Keywords: Factor endowments; Technologies; Pareto efficiency; Production possibility curves; Explicit PPC; Autarky equilibrium prices; Comparative costs; International trade models (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-52493-6_23

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