Probing Assembly Models: Exploring Innovations in Models with Perfect Complementarity

Abstract

This paper introduces and scrutinizes three groundbreaking models aimed at probing the intricacies of duopoly dynamics within perfect complement factors: (1) the spontaneous assembly model, (2) the non-spontaneous assembly model, and (3) the sequential spontaneous assembly model. This study delves into oligopoly with perfect complementarity and makes the following discoveries. First, the renowned and significant quantity competition model, the Cournot model, is equivalent to the price competition models studied in this research, the spontaneous assembly model and the non-spontaneous assembly model using ECPR. Second, the renowned and significant quantity competition model, known as the chain monopoly model, aligns with the price competition model explored in this study, termed the sequential spontaneous assembly model. Third, the three price competition models examined in this study are found to be as follows. Initially, a comprehensive investigation of the spontaneous assembly model lays the basis for a compelling argument, demonstrating that the equilibrium price of the ‘system goods’ in duopoly surpasses that of the monopoly scenario. Subsequently, we meticulously establish the mathematical equivalence between the non-spontaneous assembly model, using the ‘efficient component pricing rule’, and the spontaneous assembly model. Our focus then shifts to the sequential spontaneous assembly model, where a meticulous comparison with the simultaneous model unveils elevated equilibrium prices for the ‘system goods’. In particular, we elucidate that those industrial profits are based on the price elasticity of demand, with this sequential model yielding higher profits under conditions of inelastic demand.