Establishing long-term relationships among the members of a supply chain has become necessary to enhance the supply chain's competitiveness in a globalized environment. Besides coordinating operational decisions, such as how much and when to produce or to order, the members of a supply chain may also share financial resources or act jointly on the capital market. This is important especially when companies have unequal access to capital, for example because they are located in countries with different economic conditions and banking policies and/or ratings. The joint financing of investments across the supply chain may thus ensure the stability of production and of the flow of products to the customers. In addition, it strengthens the established relationships among the supply chain members. This study takes up these issues and presents an integrated inventory model that considers investments jointly financed by the members of a supply chain. In particular, it considers a two-stage supply chain with a single vendor and a single buyer and assumes that the vendor has the option to invest in increasing its production rate. The buyer, however, is assumed to have better access to capital, and therefore has the option to give a credit to the vendor to invest in its productivity, which is beneficial for both parties. To consider uncertainties of the production improvement investments, a success probability for the investment is considered and modeled using a beta distribution.