Barter exchange has been growingly popular in business for its advantage to liquidate excessive inventory. While barter exchange is relevant to supply chain management, little is known about its impacts on the supply chain contracting and efficiency. This study explores these issues in a two-level supply chain under a wholesale-price pull contract, where the manufacturer undertakes the inventory risk. Stackelberg equilibriums are derived when the two supply chain agents are rational and biased, respectively. We show that barter exchange encourages the retailer to provide a lower wholesale price to the manufacturer and induces the manufacturer to produce more. Barter exchange benefits the retailer and the supply chain system, thereby improving the supply chain efficiency, but may harm the manufacturer. We further examine the impacts of the supply chain agents' decision biases in barter exchange, where the retailer and the manufacturer may overestimate or underestimate the supply rate of what the retailer needs. When the retailer believes the manufacturer holds the same level of bias, the retailer's overestimation renders it to offer a lower wholesale price, thereby leading the manufacturer to produce less. This finding implies that the retailer's overestimation enhances double marginalization and reduces the supply chain efficiency. The manufacturer's overestimation leads it to produce more. However, when the biased retailer learns the manufacturer's decision bias accurately, the retailer's overestimation brings a higher wholesale price, thereby inducing a higher manufacturer's production quantity and a higher supply chain efficiency. The manufacturer's overestimation induces a lower wholesale price and a higher production quantity.