4 Cost Curves and Scale
Learn how short-run and long-run cost curves relate output, input choices, average costs, marginal cost, and economies of scale.
Short run and long run
A firm’s cost curves show how production costs change as output changes. Their shapes reflect both the production technology and input prices.
In the Short run, at least one input is fixed. In the Long run, all inputs can vary.
Short-run costs
In the short run, total cost is the sum of and :
does not change with output, while does. For example, a bakery may pay rent whether it bakes or loaves, but it uses more flour and labor as production rises.
Firms also consider costs per unit and the cost of producing additional output:
How short-run average and marginal costs relate
declines as output increases because the same is spread over more units. and are often U-shaped in the standard model. At first, better use of fixed capacity can lower per-unit costs; eventually, diminishing marginal product of the variable input tends to raise the cost of additional output.
Since average total cost includes average , average total cost lies above average , and the gap between them is average . That gap narrows as output grows.
typically rises over the range where diminishing marginal product sets in. With other input prices held constant, lower marginal product means more input is needed to produce another unit, raising its cost. Marginal cost crosses average and average total cost at their minimum points: when marginal cost is below an average, it pulls that average down; when it is above, it pulls the average up. This is the same arithmetic as a test score below or above a student’s current average.
For example, suppose total cost rises from for units to for units. The marginal cost of those additional units is per unit:
This is not the average cost of all units; it is the added cost per extra unit over that interval.
Long-run average cost
In the long run, a firm can adjust every input, including factory size and equipment, and can choose among different production setups. gives the lowest average cost attainable for each output level when the firm can choose its scale and inputs.
In the standard textbook diagram, LRAC is derived from the least-cost choices represented by a family of short-run average cost curves and forms their lower boundary. A firm committed to one plant in the short run operates on that plant’s short-run curve, even if another plant size would be more economical at its current output.
Scale and long-run cost
The shape of LRAC describes how average cost changes as the firm expands its scale.
: LRAC falls as output rises. Larger operations may use specialized equipment, divide tasks more efficiently, or spread setup and administrative costs across more units.
Constant returns to scale: LRAC remains roughly flat over a range of output. Expanding the operation does not substantially change average cost.
: LRAC rises as output rises. Coordination difficulties, communication delays, or layers of management may make a very large operation less efficient.
For example, if a manufacturer’s LRAC falls from per unit at units to per unit at units, it experiences over that range. If average cost later rises as output expands further, it experiences at those larger production levels. The minimum region of LRAC identifies the scale—or range of scales—at which average cost is lowest.
Scale effects and diminishing marginal product
are a long-run concept because all inputs can expand together. Diminishing marginal product is usually a short-run concept because one input increases while another is fixed. Thus, a firm can face rising short-run marginal cost while still enjoying long-run as it adopts a larger, more efficient plant.