In a model with endogenous number of innovating firms, we show that whether patent protection increases R&D investment is ambiguous, and depends on the market demand function and the cost of R&D. If the market size increases with number of firms, patent protection reduces R&D investment if the cost of R&D is sufficiently high, and higher product differentiation increases the possibility of lower R&D investment under patent protection. If the market size does not increase with number of firms, patent protection never reduces R&D investment. We find that welfare is lower under patent protection than under no patent protection.