What obstacles/economic barriers do stock exchanges face in developing countries?
Stock Exchanges are made of the investments, and serve as meeting point for company's ownership to be traded fast and legally. It's need and value increases with the the number of investors and companies in the market.

Several developing countries lack legislation and law enforcement that would incentivize the use of a stock exchange. On the other hand, in developing countries the ownership of the largest companies is typically in the hands of a few powerful elites or foreign investors, and neither benefit from using a stock exchange, as they are usually not looking to exchange their investments.