In a knowledge-based growth model where skilled workers are used in innovation and production, skill-biased technological change may lower average R&D productivity via an innovation possibilities frontier effect that eliminates scale effects. We show that skill-biased technological change increases the skill premium even if the elasticity of substitution between skilled and unskilled workers is less than two. Trade between developed countries promotes skill-biased technological change, thus raising wage inequality. Trade between developed and developing countries has differing effects: it induces relatively skill-replacing technological change and lowers wage inequality in the developed country but has the opposite effects in the developing country. Finally, we show that trade can stimulate or hurt economic growth.