The paper by Charles I. Jones explores the relationship between idea-based growth models and increasing returns to scale, focusing on how changes in economic scale affect long-run growth rates or income levels. It reviews three main classes of models: the Romer/Grossman-Helpman/Aghion-Howitt (R/GH/AH) models, the Jones/Kortum/Segerstrom (J/K/S) models, and the Young/Peretto/Aghion-Howitt/Dinopoulos-Thompson (Y/P/AH/DT) models. Each model has different implications for the scale effect on growth: 1. **R/GH/AH Models**: These models predict that the growth rate of per capita income is proportional to the total amount of research undertaken, leading to an exponential growth rate. However, this prediction is contradicted by empirical evidence, suggesting that population growth should not lead to accelerating per capita income growth. 2. **J/K/S Models**: These models relax the assumption that the production function for new ideas has increasing returns to scale, allowing for diminishing returns. This change results in a stable balanced growth path where the long-run growth rate is proportional to the population growth rate, while changes in research intensity affect the long-run level of income. 3. **Y/P/AH/DT Models**: These models introduce a second dimension to the R/GH/AH models by assuming that an increase in scale increases the number of available products proportionally, while the amount of research effort per sector remains unchanged. This eliminates the growth effect of scale, but population growth still affects per capita output growth. The paper concludes that all reviewed models exhibit scale effects, but these effects differ in their impact on the level of per capita income rather than its growth rate. The choice between these models depends on the specific values of parameters such as $\beta$ and $\phi$, which determine whether the economy exhibits explosive growth, a balanced growth path, or a negative scale effect on growth.The paper by Charles I. Jones explores the relationship between idea-based growth models and increasing returns to scale, focusing on how changes in economic scale affect long-run growth rates or income levels. It reviews three main classes of models: the Romer/Grossman-Helpman/Aghion-Howitt (R/GH/AH) models, the Jones/Kortum/Segerstrom (J/K/S) models, and the Young/Peretto/Aghion-Howitt/Dinopoulos-Thompson (Y/P/AH/DT) models. Each model has different implications for the scale effect on growth: 1. **R/GH/AH Models**: These models predict that the growth rate of per capita income is proportional to the total amount of research undertaken, leading to an exponential growth rate. However, this prediction is contradicted by empirical evidence, suggesting that population growth should not lead to accelerating per capita income growth. 2. **J/K/S Models**: These models relax the assumption that the production function for new ideas has increasing returns to scale, allowing for diminishing returns. This change results in a stable balanced growth path where the long-run growth rate is proportional to the population growth rate, while changes in research intensity affect the long-run level of income. 3. **Y/P/AH/DT Models**: These models introduce a second dimension to the R/GH/AH models by assuming that an increase in scale increases the number of available products proportionally, while the amount of research effort per sector remains unchanged. This eliminates the growth effect of scale, but population growth still affects per capita output growth. The paper concludes that all reviewed models exhibit scale effects, but these effects differ in their impact on the level of per capita income rather than its growth rate. The choice between these models depends on the specific values of parameters such as $\beta$ and $\phi$, which determine whether the economy exhibits explosive growth, a balanced growth path, or a negative scale effect on growth.