the links between economies and diseconomies of scale and unit costs

9.1 Location and Scale – Scale of Operations

Learning objective

Explain how economies and diseconomies of scale influence unit (average) costs and how these cost‑behaviours shape a firm’s location and relocation decisions.

Key concepts

• Economies of scale – cost advantages that arise when a firm expands output.
• Diseconomies of scale – cost disadvantages that appear when a firm becomes too large.
• Average (unit) cost – AC = TC ÷ Q, where TC is total cost and Q is output.
• Minimum Efficient Scale (MES) – the output level at which average cost is at its lowest.

9.1.1 Factors that determine location and relocation (Cambridge 9609)

Location decisions are examined at three geographic levels. The table summarises the most relevant factors for each level.

Level	Key factors (examples)
Local	Land/plant size and cost – availability of a site large enough for the desired scale. Labour market – skill mix, wage rates, union activity. Utilities – electricity, water, broadband, waste‑treatment facilities. Transport links – road, rail, port or airport proximity for inbound/outbound logistics. Local taxes, rates and any municipal incentives.
National	National infrastructure – quality of highways, rail network, ports, airports. Regulatory environment – health & safety, environmental legislation, planning permission. Size and purchasing power of the domestic market. Availability of finance, R&D support and government subsidies. Political stability, exchange‑rate risk and tax regime.
International	Trade agreements, tariffs and customs duties (e.g., EU single market, ASEAN FTAs). Currency stability and conversion costs. Reliability of global supply chains – distance to key suppliers or customers. Legal & intellectual‑property protection. Cultural differences that affect management, marketing and consumer behaviour.

9.1.2 Economies of scale

Economies can be internal (arising from the firm’s own actions) or external (derived from the industry or location).

Type	Source	Explanation & example
Technical (internal)	Plant size, specialised machinery	Larger automotive plant installs high‑capacity robots; fixed cost of the robots is spread over many more cars.
Managerial (internal)	Specialisation of management functions	Separate R&D, marketing and finance departments reduce duplication and speed decision‑making.
Financial (internal)	Access to cheaper capital	Large firms obtain bulk‑loan discounts and lower interest rates from banks.
Marketing (internal)	Bulk buying & spread of advertising costs	National retailer negotiates a lower per‑unit price for TV advertising slots.
Risk‑bearing (internal)	Product‑line diversification	A conglomerate spreads business risk across unrelated divisions.
Industry infrastructure (external)	Supplier clusters, transport networks	Silicon Valley offers a shared pool of skilled engineers, venture‑capital firms and high‑speed internet.
Knowledge spill‑overs (external)	Learning from nearby firms	Bangladeshi textile firms benefit from collective expertise in low‑cost production techniques.

9.1.3 Diseconomies of scale – common causes

• Coordination problems – communication breaks down as hierarchies deepen.
• Motivation & morale – employee alienation in very large organisations.
• Bureaucracy – excessive procedures slow decision‑making.
• Duplication of effort – overlapping departments increase overheads.
• Location constraints – higher transport costs when facilities are spread over a wide area.
• Regulatory & compliance burdens – larger firms face stricter reporting and monitoring requirements.

9.1.4 How scale affects unit costs

The average‑cost (AC) curve typically has three sections:

When a firm expands output, the total‑cost (TC) curve shifts, moving the AC curve accordingly. The downward‑sloping part reflects falling F ÷ Q (fixed cost per unit). Beyond the MES, the upward‑sloping part reflects rising marginal costs such as coordination, transport and managerial overheads.

9.1.5 Quantitative illustration

Consider the total‑cost function

\[ TC = F + vQ + \frac{Q^{2}}{2K} \]

• F – fixed cost (e.g., rent, administration).
• v – variable cost per unit (materials, direct labour).
• K – capacity parameter; a larger K gives a flatter AC curve (stronger economies of scale).

Average cost is

\[ AC = \frac{TC}{Q}= \frac{F}{Q}+v+\frac{Q}{2K} \]

Interpretation

• As Q rises, F ÷ Q falls → **economies of scale**.
• When Q becomes very large, the term Q ÷ (2K) rises → **diseconomies of scale**.

Numerical example

Output (Q)	Total cost (TC)	Average cost (AC)	Interpretation
1 000	$500 000	$500	Fixed cost per unit still high – economies not yet realised.
5 000	$2 200 000	$440	Fixed cost spread; clear economies of scale.
10 000	$4 500 000	$450	Average cost begins to rise – onset of diseconomies.
20 000	$9 800 000	$490	Diseconomies dominate; coordination & transport costs increase.

Finding the MES analytically

Set the derivative of AC with respect to Q to zero:

\[ \frac{dAC}{dQ}= -\frac{F}{Q^{2}}+\frac{1}{2K}=0 \] \[ \Rightarrow\; Q^{*}= \sqrt{2KF} \]

At \(Q^{*}\) the firm is operating at its Minimum Efficient Scale.

9.1.6 Off‑shoring and reshoring – the scale link

• Off‑shoring – moving production to a lower‑cost country to exploit cheaper labour, larger plant sites or favourable tax regimes. The cost advantage is realised only if the overseas facility can produce at a scale that spreads fixed costs sufficiently.
• Reshoring – bringing production back home to cut lead‑times, improve quality control or respond to “made‑in‑home‑country” demand. Automation can allow a smaller, high‑tech plant to achieve the same or lower average cost that previously required a large, low‑cost overseas plant.

9.1.7 Impact of globalisation on scale & location

• World‑wide markets encourage firms to increase scale to obtain **global economies of scope** (producing a range of related products in one location).
• Integrated supply chains let firms locate each production stage where the specific scale advantage is greatest (e.g., design in a high‑skill region, assembly in a low‑cost region).
• Intensified competition can force rapid expansion, raising the risk of diseconomies if coordination mechanisms are weak.

9.1.8 Determinants of the desired scale of operations

• Capital availability and financing costs.
• Technology – automation and digitalisation can shift the MES upwards.
• Demand forecasts and market size.
• Regulatory limits (environmental caps, zoning restrictions).
• Strategic objectives – market‑share ambition versus niche positioning.

Summary checklist

• Identify **internal** and **external** sources of economies of scale for the firm.
• Calculate or estimate the **MES** (\(Q^{*}= \sqrt{2KF}\)).
• Watch for early signs of diseconomies (rising AC, coordination delays, morale problems).
• Match the chosen **location** (local, national, international) with the scale needed to reach the MES.
• Consider off‑shoring/reshoring and how globalisation may shift the optimal scale.

Practice questions

1. Explain how a larger production facility can lead to lower average costs through technical economies. Provide a real‑world example.
2. Using the cost function TC = 200 000 + 30Q + Q²⁄10 000, calculate the output level that minimises average cost. Show all steps.
3. Discuss two potential diseconomies of scale that a multinational retailer might encounter when expanding its store network.
4. Identify three local, two national and two international factors that would influence a firm’s decision to locate a new plant in Vietnam rather than the UK.
5. Briefly compare off‑shoring and reshoring, highlighting how economies of scale affect each decision.

Suggested answers (teacher’s guide)

1. Technical economies arise because larger plants can install high‑capacity, automated machinery; the fixed cost of the equipment is spread over many more units. Example: Toyota’s Gigafactory uses a single high‑speed stamping press that can produce 1 200 car bodies per hour, far more than a small workshop’s 150 per hour, reducing the cost per body.
2. Average cost:
   \[ AC = \frac{200\,000}{Q}+30+\frac{Q}{10\,000} \]
   Differentiate and set to zero:
   \[ \frac{dAC}{dQ}= -\frac{200\,000}{Q^{2}}+\frac{1}{10\,000}=0 \]
   \[ \frac{1}{10\,000}= \frac{200\,000}{Q^{2}}\;\Rightarrow\; Q^{2}=2\,000\,000\,000 \]
   \[ Q\approx 44\,721\text{ units} \]
   Hence average cost is minimised at roughly **44 700 units**.
3. Potential diseconomies for a multinational retailer:
   • Coordination difficulties – synchronising inventory, promotions and pricing across hundreds of stores in different time zones can cause stock‑outs and lost sales.
   • Increased bureaucracy – additional regional management layers raise overheads and slow strategic decisions.
4. Local (Vietnam): abundant low‑cost labour; proximity to raw‑material ports; government tax incentives for foreign investors.
   National (Vietnam): developing road and rail infrastructure; relatively stable political environment.
   International: membership in ASEAN free‑trade area (lower tariffs); favourable exchange rate against the USD.
   
   Local (UK): high‑skill workforce; strong IP protection; higher land and wage costs.
   National (UK): world‑class logistics network (ports, rail); higher corporate tax rate.
   International: post‑Brexit customs procedures; stronger pound increasing import costs.
5. Off‑shoring – moves production to a lower‑cost country to exploit cheaper labour, larger scale plants and tax advantages. Scale is crucial because the cost savings are realised only when the overseas facility can operate at a sufficiently high output.
   Reshoring – brings production back home to reduce lead‑times, improve quality control and respond to “made‑locally” demand. Automation can allow a smaller, high‑tech plant to achieve economies of scale that previously required large, low‑cost factories abroad.