Optimal pricing strategies under co-existence of price-takers and bargainers in a supply chain

We investigate how the co-existence of two types of customers, price-takers, and bargainers, influences the pricing decisions in a supply chain. We consider a stylized supply chain that includes one manufacturer and one retailer, and we characterize the optimal prices of the retailer and the manufacturer. We further discuss the effects of the fraction of the bargainers in the customer population and the relative bargaining power of the bargainers on these optimal prices. Our results show that, given the wholesale price, the lowest price at which the retailer is willing to sell (ie, cut-off price) increases with the relative bargaining power of the bargainers. Both posted and cut-off prices increase in the fraction of the bargainers in the customer population. Moreover, depending on the type of negotiation cost, the variations of both prices will vary. In equilibrium, both posted and cut-off prices do not monotonically increase with the fraction of the bargainers in the customer population. When the maximum reservation price of the customers is low, and/or the negotiation costs are high, and/or the relationship between the bargainer's negotiation cost and reservation price is high, the retailer may reduce both posted and cut-off prices as the fraction of the bargainers increases.