This paper concerns the economic implications of antibiotic resistance in a global economy. The global economy consists of several countries, where antibiotic consumption creates a stock of bacteria which is resistant to antibiotics. This stock affects the welfare in all countries because of the risk that resistant bacterial strains may be transmitted. The main purpose of the paper is to compare the socially optimal resource allocation with the allocation brought forward by the decentralized market economy. In addition, a dynamic Pigouvian tax designed to implement the globally optimal resource allocation is presented.