Coordinated pricing analysis with the carbon tax scheme in a supply chain

Abstract

The carbon tax is a cost-efficient scheme to curb emissions, and it has been implemented in Australia, British Columbia, and other places worldwide. We aim to analyze its effect on dynamic pricing in a supply chain with multiple suppliers and one manufacturer. The profit-maximizing manufacturer makes final products using raw materials from suppliers with heterogeneous prices and emission rates. A two-stage game model is built over an infinite time horizon for this issue. In the first stage, suppliers face price-dependent demand to set their prices and production rates under the constraint of inventory capacity. Then, in response to the carbon tax scheme, the manufacturer evaluates the procurement prices and emission rates of suppliers to control its emission volumes and sets the sales price of its product. This article predominately focuses on the optimal pricing strategies in a decentralized supply chain. The open-loop equilibrium and Markovian Nash equilibrium for the dynamic pricing game models of both suppliers and the manufacturer are derived, respectively. The equilibrium prices of suppliers and the manufacturer can be solved based on both irreversible actions and real-time states. These two types of equilibria can be regarded as the solutions of two different models in specific situations. To analyze the effect of sourcing diversity on pricing strategies and emissions control for the manufacturer, the more general equilibrium price for the manufacturer in an n-suppliers oligopoly is studied. Numerical examples are presented to illustrate the equilibrium and its monotonicity with various parameter settings.