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Microeconomics: Long run costs and economies of scale

We have explored the concept of the costs in the short run, it is now time to determine the costs in the long run. But first, let's define the term long run. In economics, the long run occurs when all variables are not fixed. In other words, the long run for a firm is when a firm can change all of its inputs. Then, all costs are variable in the long run. In this time frame a firm is not only able to change the number of workers but also the size of its factories and the number of machines (also known as capital).

In the graph below, you can see a number of different short run average total cost (SRATC) curves that depend on the different levels of fixed inputs. At first, the SRATC curves get lower as the firm increases its size, then it flattens out. Finally,  the SRATC curves get higher. These three effects are caused by different economies of scale.
  • The leftward region on the graph represents the economy of scale, where by increasing each input by a constant increases the production function more than by multiplying the whole production function by the same constant (alpha>1).
  •  The middle region shows the constant return to scale, a firm increases its size but it's average total cost stays the same (alpha>0). 
  • The rightward region is where the long run ATC (LRATC) experiences diseconomy of scale. This is the opposite of the economy of scale, where by increasing each input by a constant results in the production function being smaller than by multiplying the whole production function by the same constant (alpha>1).

In order to obtain the LRATC, one must build a curve that envelopes the SRATC curves. Where the LRATC is tangent to some of the vertices (or minimum) of the SRATC curves.



Note that the graph above is more of a representation of what a LRATC curve with all of the different economies of scale would look like. In reality, the LRATC in the graph is just a quadratic curve, and therefore does not experience constant return to scale, though it comes close to it around its vertex. Furthermore, as you can see, some SRATC curves are not tangent the LRATC, so the latter isn't an envelope either.

Cost-Minimization Formula:

As firms try to earn as much profit as possible, one method to achieve this objective is by lowering the cost of production by decreasing the quantity produced.
  • In order to minimize the cost firms have to follow this rule: the marginal product of labor (MLP) divided by its price (Pl) must be equal to the marginal product of capital (MPK) divided by its price (Pk). Often Pl is represented by the letter w which stands for "wage" and Pk by the letter r which stands for "rent".


As a general rule, the MPL and MPK are decreasing as firms increase the number of labor and capital. Then, if




The firm should increase its labor (hire more workers) and use less capital (machines), in order to minimize its SRATC, the LRATC becomes tangent to the short run average total cost curve. If


The firm should hire less workers and employ more capital, in order to minimize its SRATC.

Reference: Mayer,David. AP Microeconomics Crash Course. Research & Education Association (2014). p 83-86. 


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