This paper develops a model of repeated product improvements across a continuum of sectors, where each product follows a stochastic progression up a quality ladder. The model explores the welfare properties of the innovation process and relates it to an alternative framework that views product innovation as a process of generating horizontally differentiated products. The authors also apply the model to issues of resource accumulation and international trade. The key findings include: 1. **Model Development**: The model describes a dynamic equilibrium where each product improves with probability \(i dt\) in a given time interval, leading to an evolving distribution of product qualities. The aggregate innovation process is smooth, with a constant growth rate driven by profit incentives in the R&D sector. 2. **Welfare Analysis**: The growth rate is calculated as \(g = t \log \lambda\), where \(t\) is the equilibrium level of R&D activity per product. The optimal growth rate is determined by maximizing utility subject to the resource constraint, and it is found that the market incentives for R&D are excessive when the steps of the quality ladder are small or large, but insufficient for intermediate steps. 3. **Quality vs. Variety**: The paper compares the quality-based growth model with a variety-based growth model, showing that they have identical reduced forms. However, the welfare implications differ, with the variety-based model exhibiting a net positive externality from each new product, leading to slower equilibrium growth. 4. **Resource Accumulation and Growth**: The model is extended to include a sector producing a homogeneous product and a second primary factor of production. It is shown that only accumulation of factors used intensively in growth-generating activities guarantees faster growth. For example, an increase in skilled labor can lead to faster growth, while an increase in unskilled labor can slow it down. 5. **International Trade**: The model is embedded in a two-country world economy to examine the long-run pattern of trade. It is demonstrated that free trade can reproduce the essential features of the integrated equilibrium, despite restrictions on factor mobility. The trade pattern follows the Heckscher-Ohlin theorem, with the home country specializing in the production of the unskilled labor-intensive good and importing the outside good. Overall, the paper provides a comprehensive framework for understanding the dynamics of quality improvement and its implications for economic growth and international trade.This paper develops a model of repeated product improvements across a continuum of sectors, where each product follows a stochastic progression up a quality ladder. The model explores the welfare properties of the innovation process and relates it to an alternative framework that views product innovation as a process of generating horizontally differentiated products. The authors also apply the model to issues of resource accumulation and international trade. The key findings include: 1. **Model Development**: The model describes a dynamic equilibrium where each product improves with probability \(i dt\) in a given time interval, leading to an evolving distribution of product qualities. The aggregate innovation process is smooth, with a constant growth rate driven by profit incentives in the R&D sector. 2. **Welfare Analysis**: The growth rate is calculated as \(g = t \log \lambda\), where \(t\) is the equilibrium level of R&D activity per product. The optimal growth rate is determined by maximizing utility subject to the resource constraint, and it is found that the market incentives for R&D are excessive when the steps of the quality ladder are small or large, but insufficient for intermediate steps. 3. **Quality vs. Variety**: The paper compares the quality-based growth model with a variety-based growth model, showing that they have identical reduced forms. However, the welfare implications differ, with the variety-based model exhibiting a net positive externality from each new product, leading to slower equilibrium growth. 4. **Resource Accumulation and Growth**: The model is extended to include a sector producing a homogeneous product and a second primary factor of production. It is shown that only accumulation of factors used intensively in growth-generating activities guarantees faster growth. For example, an increase in skilled labor can lead to faster growth, while an increase in unskilled labor can slow it down. 5. **International Trade**: The model is embedded in a two-country world economy to examine the long-run pattern of trade. It is demonstrated that free trade can reproduce the essential features of the integrated equilibrium, despite restrictions on factor mobility. The trade pattern follows the Heckscher-Ohlin theorem, with the home country specializing in the production of the unskilled labor-intensive good and importing the outside good. Overall, the paper provides a comprehensive framework for understanding the dynamics of quality improvement and its implications for economic growth and international trade.