This paper presents a model of repeated product improvements in a continuum of sectors. Each product follows a stochastic progression up a quality ladder. Progress is not uniform across sectors, so an equilibrium distribution of qualities evolves over time. However, the rate of aggregate growth is constant. The growth rate responds to profit incentives in the R&D sector. The model explores the welfare properties of this approach and relates it to an alternative one that views product innovation as a process of generating an ever-expanding range of horizontally differentiated products. The model is then applied to issues of resource accumulation and international trade. The model considers an economy with a continuum of goods indexed by ω. Each product can be supplied in a countable number of qualities. Consumers allocate spending according to a common intertemporal utility function. The model shows that each product follows a stochastic progression up the quality ladder, but the innovation process is smooth, with an index of consumption growing at a constant and determinate rate in the steady state. The model also considers the role of R&D in the economy. Entrepreneurs race to bring out the next generation of products, with successful ventures leading to further improvements. The model shows that R&D responds to profitability incentives and that the economy exhibits dynamic increasing returns to scale. The paper also explores the welfare implications of the model. It shows that the optimal growth rate can be achieved through a combination of R&D and resource allocation. The model is compared to an alternative approach that views product innovation as a process of generating an ever-expanding range of horizontally differentiated products. The two approaches yield similar results for many questions, although they differ in their normative implications. The paper also examines the relationship between the accumulation of resources and the long-run rate of growth. It shows that larger economies grow faster, and that the accumulation of factors used intensively in growth-generating activities guarantees faster growth. The model is then applied to international trade, showing that the pattern of trade is consistent with the predictions of the Heckscher-Ohlin model. The paper concludes that the model provides a useful framework for understanding the dynamics of growth and trade in a world economy with continual quality upgrading.This paper presents a model of repeated product improvements in a continuum of sectors. Each product follows a stochastic progression up a quality ladder. Progress is not uniform across sectors, so an equilibrium distribution of qualities evolves over time. However, the rate of aggregate growth is constant. The growth rate responds to profit incentives in the R&D sector. The model explores the welfare properties of this approach and relates it to an alternative one that views product innovation as a process of generating an ever-expanding range of horizontally differentiated products. The model is then applied to issues of resource accumulation and international trade. The model considers an economy with a continuum of goods indexed by ω. Each product can be supplied in a countable number of qualities. Consumers allocate spending according to a common intertemporal utility function. The model shows that each product follows a stochastic progression up the quality ladder, but the innovation process is smooth, with an index of consumption growing at a constant and determinate rate in the steady state. The model also considers the role of R&D in the economy. Entrepreneurs race to bring out the next generation of products, with successful ventures leading to further improvements. The model shows that R&D responds to profitability incentives and that the economy exhibits dynamic increasing returns to scale. The paper also explores the welfare implications of the model. It shows that the optimal growth rate can be achieved through a combination of R&D and resource allocation. The model is compared to an alternative approach that views product innovation as a process of generating an ever-expanding range of horizontally differentiated products. The two approaches yield similar results for many questions, although they differ in their normative implications. The paper also examines the relationship between the accumulation of resources and the long-run rate of growth. It shows that larger economies grow faster, and that the accumulation of factors used intensively in growth-generating activities guarantees faster growth. The model is then applied to international trade, showing that the pattern of trade is consistent with the predictions of the Heckscher-Ohlin model. The paper concludes that the model provides a useful framework for understanding the dynamics of growth and trade in a world economy with continual quality upgrading.