Radio‐frequency identification (RFID) technology has been publicized as an effective way to solve the problem of inventory misplacement in academic research as well as in the user industries. In this paper, we consider a supply chain that consists of one supplier and one retailer where the retailer is the Stackelberg leader and makes the decisions first. The consignment contract is provided such that the supplier determines the order quantity, instead of the retailer. A Non‐RFID case, a supplier investing in RFID, and a retailer investing in RFID cases are analyzed and compared. By assuming an iso‐elastic demand function and the corresponding random factor follows uniform distribution, it is intriguing to find that both supplier and retailer have the incentive to take charge of the RFID tag cost, which is not revealed in previous research. Therefore, a case of joint investment in RFID technology is formulated to find out that there are upper and lower threshold values of RFID tag cost sharing rate; that is, if the tag cost sharing rate exceeds the upper value, it is beneficial for the supplier to invest in RFID; if the tag cost sharing rate is smaller than the lower value, it is beneficial for the retailer to invest in RFID; if the tag cost sharing rate is somewhere between these two values, both supplier and retailer are better‐off. Additionally, the end customer will be better‐off if the retailer invests in RFID.