Final answer:
The private sector plays a limited role in the development of social overhead capital due to its lack of profitability, long gestation period, and the fact that the benefits accrue to all economic sectors.
Step-by-step explanation:
In the context of development of social overhead capital, the private sector plays a limited role due to several factors. Firstly, the development of social overhead capital is rarely profitable. Secondly, it has a long gestation period, meaning that the returns on investment are not immediate. Lastly, the benefits of social overhead capital accrue to all economic sectors, rather than primarily benefiting the investing entity. As a result, the private sector is not interested in taking on a major role in its development.