Chapter 4 introduces the concepts of increasing, constant, and decreasing returns to scale, and chapter 5 uses these concepts to address the question of how to determine optimal firm size, *given* the firm’s production function and the costs of inputs such as labor and capital. In chapter 5, we develop the concept of the long-run average cost curve (*LRAC*), and show that the optimal firm size occurs when long-run average cost is minimized. This occurs when long-run average cost is equal to long-run marginal cost. The “Problem Solved” box on pp. 142–143 in the textbook provides a particularly clear numerical illustration of these concepts in a case involving a constant returns to scale production function.

Technically, “returns to scale” refers to the change in *output* associated with a proportional change in all of the inputs; thus, this concept specifically applies to *production functions*. Economies of scale refers to the change in *cost* associated with a proportional change in all of the inputs; thus, this concept specifically applies to *cost functions*. However, returns to scale and economies of scale are obviously related; e.g., if a production function exhibits increasing/constant/decreasing returns to scale, then the long-run average cost function exhibits positive scale economies/no scale economies/scale diseconomies.

I confess that I have been sloppy on a couple of recent occasions by (inappropriately) using the returns to scale and economic of scale terms interchangably, most notably in the synopsis of my third lecture and during the course of a some recent email exchanges with a couple of students. Therefore, I took it upon myself to publish a corrected synopsis of the third lecture and remove problem 8 in chapter 5 from the problem set assigned for Thursday, 10/29.

Hopefully this blog entry helps to clarify not only the differences between the returns to scale and economies of scale concepts, but also how they are related.