Returns to scale: types, diagrams and causes

Meaning of returns to scale

Returns to scale describe how output responds in the long run when all inputs are increased in the same proportion, so that the scale of the firm changes while the proportions between inputs stay the same. Raise every input by 10%, say, and output may grow by more than 10%, by exactly 10% or by less than 10%. (Returns to a factor, by contrast, vary one input with the others fixed.)

Types of returns to scale

The diagrams use isoquants (curves of equal output) with labour (L) on the horizontal axis and capital (K) on the vertical axis, and a ray OR from the origin along which L and K rise in a fixed proportion. Isoquants for 50, 100 and 150 units cut the ray at points a, b and c.

The plainest case is taken first, as the yardstick, and the other two are then read as departures from it.

• Constant returns to scale (Figure 2). Output keeps exact pace with inputs: a 10% larger dose of every input gives 10% more output. Diagram: the isoquants sit at equal intervals along OR, Oa = ab = bc, since every further 50 units of output calls for the same addition to inputs. Example: opening a second identical tailoring unit beside the first.
• Increasing returns to scale (Figure 1). Output runs ahead of inputs: a 10% larger dose of every input gives more than 10% extra output. Diagram: the gaps along OR get shorter, Oa > ab > bc, since each further 50 units of output calls for a smaller addition to inputs than the last. Example: a textile unit that takes on twice the looms and workers and turns out more than twice the cloth, because at the larger size it can run a dedicated dyeing line.
• Decreasing returns to scale (Figure 3). Output lags behind inputs: a 10% larger dose of every input gives less than 10% extra output. Diagram: the gaps along OR get longer, Oa < ab < bc, since each further 50 units of output calls for a larger addition to inputs than the last.

A firm commonly passes through all three as it grows: increasing returns first, then constant, then decreasing.

Factors responsible for each

Constant returns

• The economies of larger scale have been fully reaped and the diseconomies have not yet set in, or the two balance.
• Inputs are perfectly divisible, so the firm can replicate its existing operation exactly.

Increasing returns

• Indivisibilities: some inputs (a large machine, a manager, a computer system) come in lumps and are fully used only at a larger scale.
• Specialisation and division of labour: with more workers, each can concentrate on one task and become faster.
• Technical (dimensional) factors: doubling the dimensions of a tank or furnace more than doubles its capacity.
• Managerial and organisational economies: specialists can be hired for production, finance and marketing.

Decreasing returns

• Difficulties of management: coordination, supervision and communication become harder as the firm grows; decisions slow down.
• Limited entrepreneurship: the decision-making ability at the top cannot be increased in the same proportion as other inputs.
• Diseconomies outweigh economies: beyond some size, internal and external diseconomies (management, coordination, scarcer specialised inputs) exceed the economies of scale, so output grows less than in proportion to inputs.

Conclusion

Returns to scale are increasing, constant or decreasing according as output grows faster than, in step with, or more slowly than all inputs together. Indivisibilities and specialisation explain the first phase; balance between economies and diseconomies the second; and management limits the third. Firms use this to judge how large a plant to build.