Abstract
Abstract
We study a dynamic model of quality competition in which two firms continuously invest in product quality while competing in prices. Depending on the magnitude of the quality differential relative to transportation costs, competition may be predominantly horizontal, predominantly vertical, or intermediate. We derive the corresponding Markov-perfect equilibrium conditions and show that the dynamic problem can be represented by a unified system of differential equations whose coefficients depend on the prevailing competition regime. Our main contribution is to characterize the global equilibrium dynamics generated by endogenous transitions across these regimes. We show that local equilibrium trajectories must satisfy smooth-pasting and transversality conditions in order to define globally admissible equilibria. The equilibrium selection problem is therefore one of global continuation rather than local stability. The analysis reveals a rich dynamic structure. For low transportation costs, a globally admissible equilibrium continuation originates from a vertical steady state and connects smoothly the vertical, intermediate, and horizontal regimes. As transportation costs increase, this continuation disappears before the vertical steady state itself ceases to exist. Beyond a critical threshold, a new steady state emerges within the intermediate regime. For a non-empty range of parameter values, this intermediate steady state becomes globally attractive and generates an admissible equilibrium continuation connecting the three regions of the state space. These results highlight how endogenous quality investment can induce transitions between fundamentally different forms of competition and show that the intermediate regime, usually viewed as a transient configuration in static models of product differentiation, may instead become the long-run equilibrium outcome.