Technological improvement is the most important cause of long-term economic growth. In standard growth models, technology is treated in the aggregate, but an economy can also be viewed as a network in which producers buy goods, convert them to new goods, and sell the production to households or other producers. We develop predictions for how this network amplifies the effects of technological improvements as they propagate along chains of production, showing that longer production chains for an industry bias it toward faster price reduction and that longer production chains for a country bias it toward faster growth. These predictions are in good agreement with data from the World Input Output Database and improve with the passage of time. The results show that production chains play a major role in shaping the long-term evolution of prices, output growth, and structural change.