This chapter, titled "Economic Welfare and the Allocation of Resources for Invention," by Kenneth Arrow, explores the economic welfare implications of resource allocation in the context of invention and innovation. Arrow argues that invention is broadly defined as the production of knowledge, and the optimal allocation of resources for invention depends on the technological characteristics of the invention process and the nature of the market for knowledge. Arrow discusses the classic question of whether perfect competition leads to an optimal allocation of resources, noting that while competition can achieve a Pareto optimum under certain conditions, there are three classical reasons for the failure of perfect competition to achieve optimal resource allocation: indivisibilities, inappropriability, and uncertainty. He examines each of these issues in detail, particularly the role of information as a commodity and the challenges of allocating resources in the presence of uncertainty. Arrow highlights the limitations of the real economic system in handling uncertainty, such as the lack of markets for commodity-options and the difficulties in risk-bearing. He also discusses the problems of appropriability and indivisibility in the allocation of information, which can lead to underinvestment in risky activities like invention. The chapter concludes with a discussion on the incentives for innovation in competitive and monopolistic markets. Arrow argues that the incentive to invent is lower under monopolistic conditions compared to competitive conditions, and that the realized social benefit from inventions often equals or exceeds the competitive incentive to invent. He suggests that for optimal allocation of resources to invention, government or other non-profit organizations may need to play a role, and he emphasizes the importance of nonpecuniary incentives in research and development.This chapter, titled "Economic Welfare and the Allocation of Resources for Invention," by Kenneth Arrow, explores the economic welfare implications of resource allocation in the context of invention and innovation. Arrow argues that invention is broadly defined as the production of knowledge, and the optimal allocation of resources for invention depends on the technological characteristics of the invention process and the nature of the market for knowledge. Arrow discusses the classic question of whether perfect competition leads to an optimal allocation of resources, noting that while competition can achieve a Pareto optimum under certain conditions, there are three classical reasons for the failure of perfect competition to achieve optimal resource allocation: indivisibilities, inappropriability, and uncertainty. He examines each of these issues in detail, particularly the role of information as a commodity and the challenges of allocating resources in the presence of uncertainty. Arrow highlights the limitations of the real economic system in handling uncertainty, such as the lack of markets for commodity-options and the difficulties in risk-bearing. He also discusses the problems of appropriability and indivisibility in the allocation of information, which can lead to underinvestment in risky activities like invention. The chapter concludes with a discussion on the incentives for innovation in competitive and monopolistic markets. Arrow argues that the incentive to invent is lower under monopolistic conditions compared to competitive conditions, and that the realized social benefit from inventions often equals or exceeds the competitive incentive to invent. He suggests that for optimal allocation of resources to invention, government or other non-profit organizations may need to play a role, and he emphasizes the importance of nonpecuniary incentives in research and development.