## Returns to Scale and Returns to a Factor

returns to scale

Output effect of a proportional increase in all inputs returns to a factor

Relation between output and variation in only one input

In studying production functions, two important relations between inputs and outputs are of interest. One is the relation between output and the variation in all inputs taken together. This is known as the returns to scale characteristic of a production system. Returns to scale play an important role in managerial decisions. They affect the optimal size of a firm and its production facilities. They also affect the nature of competition and thus are important in determining the profitability of investment.

A second important relation in any production system is that between output and variation in only one of the inputs employed. Returns to a factor signals the relation between the quantity of an individual input (or factor of production) employed and the level of output produced. Factor productivity is the key to determining the optimal combination of inputs that should be used to manufacture a given product. Because an understanding of factor productivity aids in the study of returns to scale, it is worth considering factor productivity concepts first.

The optimization process entails an analysis of the relation between the total and marginal values of a function. Therefore, it is useful to introduce the concepts of total, average, and marginal products for the resources employed in a production system.

The optimization process entails an analysis of the relation between the total and marginal values of a function. Therefore, it is useful to introduce the concepts of total, average, and marginal products for the resources employed in a production system.

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