Long Run Scale of Production
Economies of Scale = Increasing Returns to Scale
Diseconomies of Scale = Decreasing Returns to Scale
Also Constant Returns to Scale --- a very important assumption in economics, in general.
Something to note is that "The Law of Diminishing Marginal Returns" is a short run, not a long run concept, and doesn't apply to the topic of Economies/Diseconomies of Scale.
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Let's assume that a firm doubles its inputs. Instead of L = 1 and K = 1, let's suppose that L = 2 and K = 2. [Note that since all inputs are now "variable", this is a long run, not a short run, situation!]
When inputs (L and K) double, one of three things will potentially happen to output:
Output more than doubles (Q > 2) then AC will fall .... called Economies of Scale
Output less than doubles (Q < 2) then AC will rise ... called Diseconomies of Scale
Output exactly doubles (Q = 2) then AC is constant ... called Constant Returns to Scale
To confirm what happens to AC, first determine why TC rises when inputs double. Remember that AC = TC/Q.
[Note: Show graph of LRAC here.]