First off, we must recognize that this question assumes that people in the rich world do add to the problems of the "less fortunate." There are many scholars who would dispute this.
That said, many scholars (particularly those who study things like dependency theory or neocolonialism) who would say that people in the rich world do contribute to the problems of the less fortunate. To this way of thinking, we exploit the labor of the less fortunate as a way of making our own lives easier and more comfortable. For example, we buy products such as those made by Apple in factories in China. The argument is that these factories exploit their workers by forcing them to work long hours in poor conditions for low pay. We consumers in the rich world benefit from this by getting our products as cheaply as possible.
In this way of thinking, then, we add to the problems of the less fortunate by exploiting their labor (and the fact that they have no choice but to engage in such labor) for our own comfort and convenience.