Existence of stationary equilibrium in the markets for new and used durable goods (Q5958249)

We prove the existence of stationary equilibrium in the primary and secondhand markets for an indivisible consumer durable in a general model with stochastic degradation and endogenous scrappage decisions. Unlike \textit{J. Rust} [Econometrica 53, 783-805 (1985; Zbl 0611.90021)], we introduce transaction costs in the model as a motivation for consumer holdings of durables across multiple quality levels. Our technique allows for both multiple types of durables (e.g., Porsche and BMW) and relaxation of the single-crossing condition on consumer tastes. We provide a simple example showing how increasing transaction costs affect secondhand prices, eventually (for sufficiently costly transactions) closing the secondhand market altogether.