This is a good question that requires some understanding of the concepts of internal and external economies of scale, as well as perfect competition. Let me try to explain it in simple terms.
Internal economies of scale are the cost advantages that a firm enjoys as it expands its output and scale of production. These advantages are internal to the firm and depend on its own decisions and strategies. For example, a firm can use more efficient machinery, buy inputs in bulk, or hire specialized managers to reduce its average cost of production.
External economies of scale are the cost advantages that a firm enjoys as the industry in which it operates grows and develops. These advantages are external to the firm and depend on the actions and innovations of other firms and institutions in the industry. For example, a firm can benefit from a skilled labor pool, improved infrastructure, or better technology that are available to all firms in the industry.
Perfect competition is a market structure where there are many buyers and sellers, the products are homogeneous, there are no barriers to entry or exit, and the firms are price takers. This means that the firms have no market power and cannot influence the price of the product. They can only adjust their output to maximize their profits.
Now, let us see why increasing returns to scale due to internal economies are incompatible with perfect competition, but increasing returns to scale due to external economies are compatible with perfect competition.
If a firm experiences increasing returns to scale due to internal economies, it means that its average cost of production falls as it increases its output. This gives the firm an incentive to produce more and more, as it can lower its costs and increase its profits. However, this also means that the firm will grow larger and larger, and eventually dominate the market. This will create a situation where there are only a few large firms in the industry, or even a single monopoly. This will violate the assumption of perfect competition that there are many sellers and no barriers to entry or exit. Therefore, increasing returns to scale due to internal economies are incompatible with perfect competition.
On the other hand, if a firm experiences increasing returns to scale due to external economies, it means that its average cost of production falls as the industry grows and develops. This does not give the firm an incentive to produce more and more, as it does not affect its own costs and profits. The firm will still produce the output where its marginal cost equals the market price, which is determined by the demand and supply of the product. This also means that the firm will not grow larger and larger, and the market will remain competitive. There will still be many buyers and sellers, the products will be homogeneous, and there will be no barriers to entry or exit. Therefore, increasing returns to scale due to external economies are compatible with perfect competition.
I hope this explanation helps you understand the difference between internal and external economies of scale, and their relationship with perfect competition. If you want to learn more, you can check out these web sources that I used to create this response: Investopedia, Diferr, and Key Differences.
Source: Conversation with Bing, 11/16/2023
(1) Internal vs. External Economies of Scale: What’s the Difference? - Investopedia. https://www.investopedia.com/ask/answers/013015/what-are-differences-between-internal-and-external-economies-scale.asp.
(2) Internal Economies and External Economies(detailed explanation) - Diferr. https://diferr.com/differences-between-internal-economies-and-external-economies/.
(3) Difference Between Internal and External Economies of Scale. https://keydifferences.com/difference-between-internal-and-external-economies-of-scale.html.