We introduce non-homothetic preferences into an R&D based growth model to study how demand forces shape the impact of inequality on innovation and growth. Inequality affects the incentive to innovate via a price effect and a market size effect. When innovators have a large productivity advantage over traditional producers a higher extent of inequality tends to increase innovators’ prices and mark-ups. When this productivity gap is small, however, a redistribution from the rich to the poor increases market sizes and speeds up growth.