Game Theory Foundations: Economies of Scale or Diminishing Returns?

Before we start out foray into game theory, I'd like to do a quick review of economic efficiency framed as economies of scale versus diminishing returns for growing enterprises. In the examples provided by economics textbooks, they will often express diminishing returns as using less efficient resources in order to produce the same task (which reflects a decreasing marginal utility / benefit / revenue).

However, in the abstract, we are also told about economies of scale, where adding staff and capacity can result in productivity gains beyond what is expected (Specialization of tasks and the Model T assembly line strategy). In evaluating a scenario, how can we tell which stage we are in?

The best way to understand your efficiencies is by understanding the production bottle necks of your current factors of production. That is to say that you can fight off diminishing returns if you add resources to the weakest link of your system (similar to the idea of critical path of a PERT chart). While adding resources in general will cause you to gain diminishing returns in the one production line, it should create synergies that recoup the drop in efficiency.

Now, if you are sensitive to seemingly meaningless buzzwords like "synergy" which tend to be overused, you'll probably recoil a little as I did upon hearing that word so let's break it down to less abstract terms with an example.

Example: A factory has 200 workers working on 20 machines. The optimal ratio of workers to machines is 12 to 1 for the purposes of scheduling and capacity planning. Although adding the 21st machine will bring some benefit (versus not having the machine at all), it is clearly diminishing versus adding the 3rd machine. In this scenario, adding another 40 workers would help bring the worker / machine level up to its target concentration. Note that beyond that, adding another worker begins to diminish the benefit of workers and the value of adding a machine starts to increase again.

Now assume that you have a limited number of resources to apply to your production. What mix of workers to machines will you have?
This introduces the idea of production-possibility frontiers which we will discuss in the next post.