A By-Production Approach to Deriving the Production Possibility Frontier and the Shadow Prices of CO₂ Reduction

<title>Abstract</title> <p>This paper develops a novel method to derive an explicit Production Possibility Frontier (PPF) for desirable and undesirable outputs within a by-production framework. We formulate a constrained optimization model that, under proven regularity conditions, ensures a unique PPF where technology operates on its efficient boundary for both types of outputs. Marginal abatement costs (MACs) are obtained directly as PPF slopes, consistent with the marginal rate of transformation, and without requiring the arbitrary directional vectors used in directional distance function approaches. We apply the method to panel data for sixteen Asia-Pacific economies from 2010 to 2019, estimating an explicit PPF and corresponding MACs. These estimates capture the short-run opportunity costs of emissions abatement along a fixed technological frontier, rather than engineering costs of fuel switching or technological change. The framework offers policymakers a comprehensive view of tradeoffs between output and emissions at scales ranging from marginal reductions to economy-wide transitions.</p>