Economies and Diseconomies of Scale

The long run and the long-run average cost

Economists split time into two periods, and the split is not measured in days or years.

• Short run: at least one input is fixed. A bakery can hire extra staff, but it cannot build a bigger kitchen overnight.

• Long run: all inputs can be changed: labour, machinery, premises, even the number of plants.

In the long run a firm chooses its scale, meaning the overall size of its operation. For each possible scale there is a lowest possible cost per unit. The curve joining these lowest costs is the long-run average cost (LRAC) curve.

Average cost is total cost divided by output:

Notice that total cost almost always rises when output rises. The question is whether it rises faster or more slowly than output. If output doubles but total cost less than doubles, average cost falls.

The answer to the last step: average cost rose from €16 to €18, which is $\frac{2}{16} \times 100 = 12.5\%$ higher. This is diseconomies of scale.

Economies of scale: internal and external

Why would a bigger firm have a lower cost per unit? The reasons divide into two groups.

Internal economies of scale

Internal economies come from the growth of the firm itself. They are under the firm's own control.

The principle of specialisation is behind many of these: when workers and machines concentrate on narrow tasks, output per worker rises and cost per unit falls.

External economies of scale

External economies come from the growth of the whole industry or the region, not of one firm. A single firm does not control them, but it benefits from them.

• A pool of skilled labour develops because many firms in the same area need the same skills (for example, aerospace engineers around Shannon).

• Supporting industries appear nearby: suppliers, repair firms, specialist transport.

• Better infrastructure is built: a new motorway, a port upgrade or a broadband network cuts delivery costs for all firms.

• A reputation for quality attaches to a region or industry.

Diseconomies of scale

Growth does not lower costs for ever. Beyond a certain size, average cost starts to rise. Common causes:

• Communication problems: more layers of management mean slower decisions and misunderstood instructions.

• Coordination problems: it is harder to organise several plants, departments or sites.

• Worker motivation: in a very large firm, employees may feel anonymous, and productivity and quality can fall. Industrial disputes may become more likely.

• Bureaucracy: more rules, forms and meetings use up resources without producing output.

• Overstretched resources: buying very large amounts of an input may push its price up, for example if the firm is the main buyer of local milk or labour.

External diseconomies also exist: if an industry or region grows too much, congestion, higher rents and higher wages raise costs for every firm (think of traffic and housing costs in a crowded city).

Limiting diseconomies

Management can act to slow the rise in average cost:

• Decentralise: give plant or regional managers more decision-making power.

• Improve communication: better IT systems, regular meetings between sites.

• Split into smaller units or divisions: each one keeps a manageable size.

• Motivate staff: profit-sharing, training, involving workers in decisions.

The LRAC curve and the minimum efficient scale

Putting economies and diseconomies together gives the typical U-shaped LRAC curve, with three zones.

• Falling part: economies of scale (LRAC falls as Q rises).

• Flat bottom: constant returns to scale, where LRAC does not change.

• Rising part: diseconomies of scale (LRAC rises as Q rises).

If MES is large compared with the size of the market, only a few firms can reach it. That is why industries such as electricity supply or pharmaceuticals are dominated by a small number of large producers.

The answer: $6.50 \times 50{,}000 = \text{€}325{,}000$, against $6.00 \times 30{,}000 = \text{€}180{,}000$. Total cost is higher, and that is no contradiction. Total cost nearly always rises with output. Diseconomies of scale refer to the cost per unit.

Finding the minimum LRAC with calculus (Higher Level)

When the LRAC is given as a function, find the minimum by differentiating and setting the derivative equal to zero.

Check: $300 - 120 + 40 = \text{€}220$, which is higher than €210. This fits the economies-of-scale range.

Try it yourself: move the sliders to see how the shape changes.

Using the ideas: mergers, small markets and plant size

Examination questions at Higher Level often ask you to discuss or evaluate a business or policy decision using scale ideas. Use this approach:

1. State the cost effect: is the firm below or above its MES? Which economies or diseconomies are involved?

2. Quantify if you have numbers (savings, payback period).

3. Weigh up other factors: employment, competition, customers, risk.

4. Conclude with a judgement that depends on the evidence.

Mergers and the small Irish market

A merger joins two firms into one. If both firms are well below MES, a merger can help them reach it: unit costs fall, so the firm can charge lower prices or earn higher profit.

Ireland has a small domestic market, so many Irish firms cannot reach MES by selling at home alone. Membership of the EU single market, with over 400 million consumers and no tariffs between member states, lets firms sell more and so reach MES by exporting. Reaching MES is therefore important for competing in export markets.

Possible disadvantages of mergers:

• Diseconomies of scale if the merged firm becomes too large to manage.

• Integration costs: different systems, cultures and brands.

• Job losses, especially in a region that depends on one employer.

• Less competition if the merged firm gains too much market power, which can mean higher prices for consumers.

Payback period

When a decision costs money now and saves money each year, the payback period shows how long it takes to recover the cost:

Back to the start: Aoife's cost per loaf will probably fall if she triples output, because she can buy flour in bulk and use her oven more fully (internal economies). If she keeps growing into four counties, management and coordination problems may eventually raise her cost per loaf again.

Summary

• The long run is the period in which all inputs can change. The LRAC curve shows the lowest cost per unit at each scale.

• Economies of scale: LRAC falls as output rises. Internal economies (technical, purchasing, managerial, financial, marketing, risk-bearing) come from the firm's own growth. External economies (skilled labour, suppliers, infrastructure) come from the growth of the industry or region.

• Diseconomies of scale: LRAC rises because of communication, coordination, motivation and bureaucracy problems. Management can limit them by decentralising, improving communication and motivating staff.

• The LRAC curve is typically U-shaped. The minimum efficient scale (MES) is the lowest output at which LRAC is at its minimum. With a cost function, find it by solving $\frac{d(LRAC)}{dQ} = 0$.

• $AC = TC/Q$. Total cost normally rises with output, even while average cost falls.

• Scale helps determine the size of firms: where MES is large relative to the market, firms must grow (or merge) to compete, whereas diseconomies of scale set an upper limit on a firm's efficient size.

• In evaluation questions, quantify the effect (savings, payback period), consider non-cost factors, and finish with a judgement.

Key terms: long run, scale, LRAC, economies of scale, diseconomies of scale, internal economies, external economies, constant returns to scale, minimum efficient scale (MES), merger, single market, payback period.