Does Pooling Purchases Lead to Higher Profits?

Consider two buyers facing uncertain demands who need to purchase a common critical component from a powerful sole-source supplier. If the two buyers pool their demands and purchase from the supplier as a single entity, will they necessarily earn higher profits than purchasing separately? We show that when a powerful supplier extracts profits from the buyers through optimal contract design, the demand variability reduction achieved by pooling can harm the buyers because it makes extracting profits easier for the supplier. We characterize cases when pooling is disadvantageous and also provide insights into when it is still advantageous. Our result is in contrast to the case where the price of the component is exogenous (typically assumed in most of the pooling literature), in which case pooling demands is always beneficial for the buyers.