The possible co-existence of spot and contract market that can emerge in the presence of quality issues with a number of growers and processors in each stage is something that has largely remained an open question in the literature. This paper is an attempt to fill this void. We use a straightforward two-stage Cournot oligopoly model with specific demand and cost functions. In the first stage, processors decide simultaneously whether or not to set an incentive contract. The second stage is the stage in which growers choose their levels of quantity and quality based on the industry structure developed in the first stage. With the help of numerical simulations we conducted the study of the equilibrium structures. Our results suggest that for a wide range of number of participants in both markets, participation in both markets constitutes a Nash equilibrium for the model.