3.3 — Long-Run Production Costs

In the long run, all inputs are variable, and firms can adjust their scale of production. This flexibility allows firms to minimize costs by choosing the most efficient input combination for a given level of output.

Economies and Diseconomies of Scale

As firms increase production, their costs per unit may decrease, remain constant, or increase:

1. Economies of Scale: Long-run average total cost ($LRATC$) decreases as output increases. This occurs due to factors like specialization, bulk purchasing, and improved technology.
2. Constant Returns to Scale: $LRATC$ remains constant as output increases. This happens when a proportional increase in all inputs leads to the same proportional increase in output.
3. Diseconomies of Scale: $LRATC$ increases as output increases. This results from inefficiencies like communication breakdowns or coordination challenges in large firms.

In simpler terms, there are three possible outcomes, given in the following example: Assume a firm is producing 100 bikes with a fixed number of resources (workers). If the firm decides to double the resources, what happens to the number of bikes?

There are three possibilities:

1. It will double (constant return to scale)
   1. Both resource and output increase equally
2. It will more than double (increasing returns to scale)
   1. Output increase is greater than resource output
3. It will less than double (decreasing returns to scale)
   1. Output increase is less than resource output

Long-Run Average Total Cost (LRATC) Curve

The $LRATC$ curve is derived from a series of short-run ATC curves, each representing a specific plant size or scale of production. The $LRATC$ is U-shaped because:

• Initially, economies of scale reduce costs as production expands.
• Eventually, due to the Law of Diminishing Marginal Returns, diseconomies of scale increase costs as production grows too large.

$LRATC=\frac{\text{Total Cost in the Long Run}}{\text{Output}}$