What is diminishing returns?

Diminishing returns describes how adding more of one input, while holding the others constant, produces smaller and smaller gains. Adding workers to a fixed workshop is the standard picture. It matters because it explains why there is a point where adding more stops being worth the cost.

How it works

At first, each extra unit of an input has plenty of other resources to work with, so its contribution is large. As more are added, they begin to share the same fixed machines, space or attention, and the added output per unit shrinks. The total still rises, but more slowly, and in extreme cases it can even fall.

The decision rule that follows is to keep adding the input while the extra output is worth more than the extra cost. The best amount is where the extra output of one more unit just equals its cost. Beyond that point, each added unit costs more than it brings in.

Example

Say a workshop with one machine produces 10 items per day with one worker, 18 with two, 24 with three, 28 with four and 30 with five. The extra output from each added worker is 10, 8, 6, 4 and 2. If a worker costs 5 items' worth of value per day, the fourth worker still adds 4, which is nearly break-even, and the fifth adds only 2, which is less than the cost. The workshop should stop at about four workers. The figures are an illustration.

How to model it in Machinations

Create a Pool called Workers fed by a Lever, and a Converter that turns workers into output at a rate set by a Register. Write the Register so that the output per worker falls as the number of workers grows, for example by dividing by one plus a fraction of the worker count. Add a Drain for wage cost. Play with the number of workers from one to eight and chart output and net value to find where the extra gain runs out.