Monopoly with differentiated final goods and heterogeneous markets

This work attempts to characterise the dynamic properties of a nonlinear model in which a monopolist produces a fixed amount of an intermediate good. The firm employs this good in producing two vertically differentiated final commodities, sold in two distinct markets. Consumers’ preferences are described by quasi-linear and quadratic utility functions respectively yielding isoelastic and linear demand functions. In addition, we assume that the monopolist adopts a gradient adjustment rule based on profit variation to adjust its choice about the amount of intermediate good to employ in the production of each final good. Two alternative scenarios emerge: in the first, there exists coexistence of two markets; in the second, the monopolist specialises on the production of a single final good. The dynamics show that the elasticities of market demands play an ambiguous role in affecting the stability of the equilibrium, whereas the speed of adjustment unambiguously destabilises the system. Moreover, the article investigates the role of the productive capacity and the gap in marginal costs in defining the different scenarios. In particular, economic dynamics may be chaotic and/or multiple attractors may appear.