Firm Behaviour
Senior 4 · Economics
Firm Behaviour
Lesson 4 of 5
30 min
In September 2023 Equity Bank Rwanda acquired Cogebanque, and the number of banks in Rwanda fell by one, to 14 (National Bank of Rwanda, 2024). Across the whole economy, NISR's Establishment Censuses show that between 2020 and 2023 the number of large enterprises (over 100 workers) rose from 303 to 421, and the number of people they employed from 123,354 to 196,999.
Firms grow by expanding their own plants and by joining with other firms. Growth matters because size changes costs: up to a point, bigger firms produce more cheaply; beyond it, they become harder to run. This lesson studies the long run, when a firm can choose the size of its plant.
Definition
Long run: the period in which a firm can change all its inputs, including the size of its plant.
Long-run average cost (LRAC): the lowest average cost of producing each output when the firm can choose any plant size. It is called an envelope curve because it wraps around the short-run average cost (SRAC) curves of all possible plants.
Economies of scale: falls in long-run average cost as the scale of production increases. Diseconomies of scale: rises in long-run average cost as scale increases further.
Minimum efficient scale (MES): the lowest output at which LRAC reaches its minimum.
A firm planning a new plant can choose a small, medium or large one. Each size has its own U-shaped SRAC curve. For any output, the firm picks the plant that produces it most cheaply; the LRAC curve joins these lowest costs. In the illustrative diagram below, , and each plant's curve is , which touches LRAC at .
Reading the diagram. (1) LRAC falls up to 10 thousand units (economies of scale), is lowest at 10 (the MES), and rises after that (diseconomies of scale). (2) Each SRAC touches LRAC once and lies above it everywhere else: in the long run the firm can always do at least as well as with a fixed plant. (3) To the left of the MES, the small plant touches the LRAC to the left of its own lowest point (at Q = 4, cost Frw 37.20, while the plant's own minimum is Frw 35.40 at Q = 5.5). It is cheaper to run a slightly larger plant below capacity than a small plant at full stretch.
Worked example 1: reading the LRAC equation
(a) Average cost at 4, 10 and 16 thousand units: ; ; francs.
(b) Gain from growing from 4 to 10 thousand units: average cost falls by .
(c) Minimum efficient scale (using calculus): thousand units.
(d) Meaning for the industry: if the whole market buys only 15 thousand units a month, there is room for just one firm at the MES. A small market can support few efficient firms, which is one reason markets in small economies tend to have few large firms.
Internal (organic) growth: a firm expands its own capacity by reinvesting profit, borrowing, issuing shares, launching new products or entering new markets. It is slower but keeps control and culture intact.
External growth: a firm joins with another. In a merger (amalgamation) two firms agree to combine into one; in a takeover (acquisition) one firm buys control of another.
| Type of integration | Joins firms… | Example | Main motive |
|---|---|---|---|
| Horizontal | At the same stage of production in the same industry | One bank acquiring another (Equity Bank Rwanda and Cogebanque, 2023) | Economies of scale, larger market share |
| Vertical backward | With a supplier at an earlier stage | A tea factory buying tea estates | Secure supplies and quality of raw material |
| Vertical forward | With a buyer at a later stage | A coffee roaster opening its own coffee shops | Secure outlets; capture the retail margin |
| Conglomerate (diversified) | In unrelated industries | A cement maker buying an insurance company | Spread risk across markets |
Effects of mergers. They may lower costs through economies of scale and bring better management and finance. But they can also reduce competition, raise prices, close branches and cut jobs. For that reason, regulators review large mergers; in banking, the National Bank of Rwanda supervises every bank.
Definition
Internal economies of scale: cost savings that arise inside one firm as it grows. External economies of scale: cost savings that all firms in an industry or area enjoy as the industry grows (for example, a pool of trained workers or specialised suppliers).
Example: a bakery that buys flour by the lorry-load gets a discount (internal); every bakery in a town benefits when a flour mill opens nearby (external).
| Internal economy | How it lowers average cost |
|---|---|
| Technical | Large machines that cannot be divided (a cement kiln); the "increased dimensions" of tanks and lorries; linking processes; more specialised machines |
| Managerial | Specialist managers for finance, marketing and production instead of one owner doing everything |
| Commercial (marketing) | Discounts for buying inputs in bulk; advertising and transport costs spread over more units |
| Financial | Large firms borrow more easily and at lower interest; they can sell shares |
| Risk-bearing | Several products and markets spread the risk of a fall in one |
| Research and welfare | Research costs spread over more output; better staff facilities raise productivity |
External economies come from the growth and concentration of the industry: skilled labour, ancillary suppliers, specialised banks and repair services, shared infrastructure and information (lesson 2). Because they benefit every firm, they shift the whole LRAC curve downwards, whereas internal economies are a movement along a firm's LRAC.
Diseconomies of scale. Internal: management becomes stretched; messages pass through many layers and decisions slow down; workers feel remote and motivation falls; disputes are larger. External: as an industry crowds into one area, land rents, wages and input prices are bid up, and congestion and pollution raise costs; these shift the LRAC upwards.
Worked example 2: the "increased dimensions" economy
A cube-shaped storage tank has sides of length . The material needed depends on its surface area, ; what it holds depends on its volume, .
Double the side to : surface , four times as much material; volume , eight times as much storage.
Cost per litre stored: of what it was. Doubling the size halves the material cost per litre. The same geometry explains why large lorries, pipelines, silos and kilns carry or process goods more cheaply per unit.
Warning
Economies of scale are not the same as increasing returns to a factor. Economies of scale are a long-run fall in average cost as all inputs grow. A falling short-run AVC (because MP is rising) is a short-run effect with a fixed plant. And a big firm is not automatically cheaper: past the MES, diseconomies raise its average cost.
Tip
"T-M-C-F-R" for internal economies: Technical, Managerial, Commercial, Financial, Risk-bearing. External economies move the whole LRAC down; internal economies move the firm along it.
Important
Discuss. When one bank acquires another, customers may gain from a larger branch network and cheaper services, or lose from less competition. Which effect is likely to be stronger in a country with only 14 banks? What should a regulator look for?
tutor2u, "Key Diagrams - Long Run Average Cost (Economies and Diseconomies of Scale)". Watch how the LRAC curve is drawn, where the minimum efficient scale lies, and why internal economies move a firm along the curve while external economies shift the curve down.
Practice
Key points
Sources and credits
Written by Ganzaa: the text, the LRAC diagram (drawn to scale from the cost equations), the tables, the worked examples and the practice items. The cost equations are illustrative.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.
Quick check
Equity Bank Rwanda's acquisition of Cogebanque in 2023 joined two banks. What kind of integration is this?
