It is well known that the set of feasible net production points is convex if the underlying production functions are of the constant-returns, no-joints-products type and if there are no technological externalities. It is now shown that if there are public intermediate goods and if at least one public intermediate good is essential to the output of each final good, then the set of production possibilities is convex and the transformation surface strictly concave, and this is so whatever the numbers of primary factors, final goods, and public intermediate goods.