Joint pricing and quality decision model under stochastic reference quality effect

This paper uses stochastic control theory to study a monopolist's time-varying policies regarding price and product quality in the presence of stochastic reference quality effect. A novel feature of our model is to allow for some randomness in the evolution of consumers' reference quality levels to capture intertemporal heterogeneity of consumers or exogenous shocks. We first derive the optimal explicit contingent (closed-loop) strategies by Hamilton-Jacobi-Bellman equation based on the assumption that the reference quality information is available. Our results show that the monopolist benefits from higher price and higher quality policies compared with the results in the deterministic model. In the long run, our results suggest that, on average, consumers purchase a product with a lower price per unit of quality and are relatively more sensitive to changes in quality than in price under stochastic reference quality effect. Additionally, we consider alternative committed (open-loop) policies when reference quality information is not unobtainable. We explicitly characterize the probability distribution of reference quality under both strategies and numerically highlight the value of acquiring reference quality information. Numerical study further shows that expected steady-state price, quality, and quality-price ratio increase with the intensity of reference quality effect and with the marginal contribution of quality on demand, but decrease with the customers' memory and with the monopolist's patience.