Increasing Returns to Scale and the Long Run

In microeconomics, we think of diminishing returns as a short run thing. In the long run, all inputs can be increased or decreased in proportion. Reductions in the marginal productivity of labor, due to increasing the labor input, can be offset by increasing the tools and equipment the workers have to work with. How will that come out, on net? The answer is -- "it all depends!"

In the long run we define three possible cases:

Decreasing returns to scale

If an increase in all inputs in the same proportion k leads to an increase of output of a proportion less than k, we have decreasing returns to scale. Example: If we increase the inputs to a dairy farm (cows, land, barns, feed, labor, everything) by 50% and milk output increases by only 40%, we have decreasing returns to scale in dairy farming. This is also known as "diseconomies of scale," since production is less cheap when the scale is larger.

Constant returns to scale

If an increase in all inputs in the same proportion k leads to an increase of output in the same proportion k, we have constant returns to scale. Example: If we increase the number of machinists and machine tools each by 50%, and the number of standard pieces produced increases also by 50%, then we have constant returns in machinery production.

Increasing returns to scale

If an increase in all inputs in the same proportion k leads to an increase of output of a proportion greater than k, we have increasing returns to scale. Example: If we increase the inputs to a software engineering firm by 50% output and increases by 60%, we have increasing returns to scale in software engineering. (This might occur because in the larger work force, some programmers can concentrate more on particular kinds of programming, and get better at them). This is also known as "economies of scale," since production is cheaper when the scale is larger.

In introductory economics, we usually discuss these long run tendencies in the context of cost analysis, rather than marginal productivity analysis. However, increasing returns to scale, in particular, creates some complications for the application of marginal productivity thinking. Thus, I think there may be something to gain by exploring how increasing returns to scale goes together with marginal productivity. To keep it as simple as possible, we will look at a numerical example of a two-person labor market and a fictitious product that is produced with increasing returns to scale. Economists often like to talk about the production of "widgets," so our fictitious industry is the widget-tying industry.