Long-run average cost envelopes possible plants

The firm chooses a plant and an operating point.

Each short-run ATC curve belongs to a particular plant size. Long-run average cost shows the lowest attainable average cost for each output when the firm can choose among plants. The firm need not operate every plant at its own minimum. It chooses the plant that minimizes cost for the intended output.

Imagine three kitchens: small, medium, and large. At low output, the small kitchen may have the lowest average cost because the larger spaces carry unused capacity. At medium output, crowding raises the small kitchen’s cost and the medium plant becomes cheaper. At high output, the large kitchen may be least costly. LRAC traces the lowest available point across all plant choices.

The envelope is a planning curve. Once the firm builds a particular plant, it operates on that plant’s short-run ATC until it can adjust capacity again. A firm expecting 500 units chooses a different plant than one expecting 5,000. Movement along LRAC therefore combines a change in output with an optimal change in all relevant inputs.

Economies of scale occur when output grows more than proportionally to all inputs and long-run average cost falls. Specialization, indivisible equipment, and spreading design or network costs can create them. Constant returns to scale mean output changes in the same proportion as inputs. Diseconomies of scale arise when coordination, communication, and monitoring problems make output grow less than proportionally, raising LRAC.

Returns to scale describes a physical experiment: change every input by the same percentage and observe output. Economies of scale describes the associated cost result as the firm adjusts all inputs optimally. In the standard setting they point in corresponding directions, but keep the language clear: one compares inputs with output. The other compares output with long-run average cost.

If all inputs rise 50 percent and output rises 80 percent, the firm has increasing returns to scale over that range. Constant returns would raise output 50 percent, not double it. This proportional comparison differs from marginal product, which changes one input.

Increasing returns can result from specialization and indivisible capital. A large machine may be too costly for small output but efficient when used heavily. Diseconomies can arise when information must pass through more managerial layers or when local decisions become harder to coordinate. These are long-run scale mechanisms, not short-run crowding around a fixed oven.

Two experiments, two concepts

Holding a factory fixed, adding workers eventually lowers MP: diminishing marginal returns. Building a larger factory while increasing labor, machines, and space 40 percent raises output 60 percent: increasing returns to scale. Both can be true because the first changes one input and the second changes all inputs.

Minimum efficient scale is the smallest output at which long-run average cost reaches its lowest sustainable level. If it is small relative to market demand, many firms can operate efficiently. If it is large relative to demand, one or a few firms may serve the market at lower cost, contributing to natural monopoly or oligopoly.

On the exam, underline “all inputs” or “one variable input.” Then compare percentages rather than raw amounts. A 20-unit output increase is not enough to classify returns without knowing the initial output and input changes.