7.5 Costs in the Long Run

Production Costs and Economies of Scale

Production costs behave differently depending on whether a firm can adjust all of its inputs. In the long run, every input is variable: a firm can build a bigger factory, hire more workers, or completely restructure how it produces. Understanding how average costs change as a firm scales up (or down) is central to predicting firm size, pricing, and industry structure.

Relationship Between Production Costs and Economies of Scale

As a firm increases its output in the long run, its long-run average total cost (LRATC) can move in three directions:

• Economies of scale occur when LRATC falls as output increases. This happens because larger firms can specialize workers into narrower tasks, negotiate volume discounts on inputs, and spread large fixed investments (like R&D or specialized machinery) over more units of output.
• Diseconomies of scale occur when LRATC rises as output increases. At very large scales, coordination becomes harder, communication slows down, and management layers multiply. Inputs that were once cheap may also become scarce, driving up their price.
• Constant returns to scale occur when LRATC stays flat as output increases. Doubling all inputs exactly doubles output, so per-unit costs don't change.

The minimum efficient scale (MES) is the smallest level of output at which a firm reaches its lowest possible long-run average cost. Any firm producing below the MES is at a cost disadvantage compared to larger competitors. Industries where the MES is very large relative to market demand tend to have fewer firms (think utilities or aircraft manufacturing).

Long-Run and Short-Run Average Cost Curves

Short-run average cost (SRAC) curves show the average cost of production when at least one input is fixed (usually the size of the plant or factory). Each SRAC curve corresponds to a different plant size. These curves are U-shaped because of the law of diminishing marginal returns: at first, adding variable inputs to a fixed plant improves efficiency, but eventually each additional unit of input adds less and less output, pushing average costs back up.

The long-run average cost (LRAC) curve traces the lowest possible average cost for every level of output, assuming the firm can choose any plant size. Graphically, it's the "envelope" that just touches the bottom of each SRAC curve. The LRAC is also U-shaped, but for a different reason than the SRAC: its shape reflects economies and diseconomies of scale, not diminishing returns.

A few key relationships to keep straight:

• Each point on the LRAC corresponds to the SRAC of the optimal plant size for that output level.
• The long-run marginal cost (LRMC) curve shows the added cost of one more unit when all inputs can adjust. It intersects the LRAC at its minimum point, which is the MES.
• At the MES, the firm is on the lowest point of both the LRAC and the particular SRAC curve for the optimal plant size at that output.

Production Technology and Input Prices

Input Prices and Choice of Production Technology

Firms don't just pick a random way to produce. They choose the combination of inputs (labor, capital, land, etc.) that minimizes cost for a given level of output. When input prices change, the cost-minimizing combination shifts.

Here's how that works in practice:

1. Substitution effect: If the price of one input rises (say, wages increase), firms substitute toward relatively cheaper inputs. A factory might replace some assembly-line workers with automated machinery. Conversely, if capital becomes more expensive, firms lean toward more labor-intensive methods.
2. Scale effect: A change in input prices also changes the overall cost of production, which can shift the firm's optimal output level. If wages rise significantly, a firm's costs go up, and it may choose to produce less, which in turn affects how much of each input it uses.

These adjustments are easier in the long run than the short run. In the short run, firms face constraints like existing leases, long-term supplier contracts, and equipment that can't be swapped out quickly. A restaurant locked into a five-year lease can't simply move to a smaller space when rent feels too high relative to revenue.

Over time, though, all contracts expire and all equipment can be replaced. That's exactly what makes the long run "long": it's the time horizon over which every input becomes variable and every production decision is on the table.